9mo is self-weaning but won't eat solids

While it is absolutely worthwhile to follow up on your pediatrician's concerns around low muscle tone, I would say on the food front that your daughter's experience is consistent with my kids'. The mantra at the time was "solids before one are just for fun!" and our older child didn't really eat much actual food until he was 13 or 14 months. (He did continue to nurse twice a day, and we introduced cow's milk in a cup at one, since he wouldn't take a bottle at daycare; as a tween he is still a picky eater who sometimes opts out of meals.) Both of my kids settled onto their long-term growth curves around 9-12 months, and these were not the same as their early curves--both are now right around 30th percentile for height and lower for weight, while one was down in the single digits as a baby and the other was up at the 60th percentile till close to a year. (Their percentiles have remained pretty consistent for the years since, though--they are now 7 and 10, and 30th percentile is in keeping with parental genes). So I would not necessarily worry about the food intake unless your daughter is underweight or there are other specific medical concerns. In your shoes, I'd focus on continuing to offer new foods without stressing too much about how much is being eaten and meet with the physical therapist to get muscle tone assessed, but otherwise wait to see how things look at the 12-month checkup. Also be mindful of her physical development--for instance, it's not uncommon for 9-month-olds to drop down the growth curve if they've recently started crawling (or are about to crawl). Other developmental milestones can affect that too since they burn calories that might otherwise fuel growth.

My son had low muscle tone around his lips and was a very picky eater. He also drooled a lot. At that age, he only ate mush. We did not do baby led weaning. For a long time he preferred very soft and slippery food like yogurt, udon noodles, tofu, and fruit purees. We thought he was just picky but on hindsight it was probably because he had a hard time chewing the other foods. So maybe you can offer food that just goes down easier? Also we spaced out the solids away from his bottle, so we would give him his bottle in the morning, wait a few hours before serving him solids, or else we would serve him solids and then offer him a bottle later. Nobody likes to eat when they are already full, and I'd bet your baby would be more willing to try more solids if she sat down hungry.

We went through a similar weight drop when mine was around 9 months. We were doing baby led weaning and I thought it was going great! He clearly enjoyed it and I loved that he was getting exposed to so many fruits and veggies -- though like you said, he was mostly gnawing, so it didn't really result in much food being consumed. I was shocked to learn that he had stopped putting on weight, because he was still breastfeeding and as another commenter noted, my understanding was that "solids before one are just for fun." I was really viewing it as an activity more than nourishment. 

Once we learned he was dropping weight, I took a step back and realized that pretty much everything I put in front of him was low in fat and calories -- I remember lots of cucumber and bell peppers, because he liked them and they were so easy to chop up. What helped us was simple recipes you cook in mini muffin tins, which are easy for them to hold but you can pack in heftier ingredients, like greek yogurt for instance.   
Our go-tos were egg cups and oatmeal cups. There are endless ways to change up the ingredients, and they freeze really well so you can make a big batch and thaw as you go. 
Here are two examples:
https://babyfoode.com/blog/toddler-breakfast-egg-cups-4-tasty-ways/ 
https://www.healthylittlefoodies.com/fruity-oat-breakfast-bites/

Btw, he's almost 4 now, and it still takes a ton of food to keep up with him! He's still a bit of a stringbean, but it seems like his body just burns through food really quickly and needs to eat often, and amply :) Good luck to you guys!

When my son fell off the weight chart, his Kaiser pediatrician referred us to a nutritionist. He's currently a teen, so baby led weaning wasn't really a thing then. We added fats into his food - lots of avocado, olive oil, and butter. We also had to make a fortified milk with condensed milk (we didn't have a lot of success with that). But she gave us a lot of good ideas to try. Maybe along with OT, consulting a nutritionist about how to feed her good fats might help as well. It helped us. But in the end, I just have a very very slender child. 

I didn't have this exact issue with my son, but he ONLY wanted to be nursed at your child's age and also refused to be fed. He was a big guy and I was suffering. What worked was 1) allowing him to feed himself, 2) trying many many different foods. Eventually lamb babyfood turned him into a kid who'd sometimes allow himself to be fed by spoon. Also, feeding while sitting in my lap. While his dad joked around, etc. Give her those baby biscuits, peas, cut up pasta, whatever. Just try everything. Put a sheet under her chair and let her make a mess. If it's FUN she may be more inclined. Make sure she's actually eating. Try small pieces banana. There's a lot of info about this online - check youtube etc. Clever ideas. As my pediatrician said at the time, "babies are not suicidal - they will eventually eat."  You might also have someone other than mom feed her - while you're away. 

It’s great that your pediatrician is being cautious and keeping an eye on things but I’ll echo that I wouldn’t get too worried as different babies have very different curves with solid food intake. We also love BLW as a fun, exploratory process but my 11 month old was very slow to actually ingest much and while we began at 6 months, eating significant amounts has really only just taken off and is incredibly variable. If you want to try to encourage more you could offer the spoon or pre-chewed bites on your finger without forcing— our daughter finds that fun too! Remember how small their stomachs actually are, however, and respect that she’s done when she turns her face away— you want to try to avoid any coercion around feeding if you can  

Breastfed babies also have slightly different growth curves and will often seem to plateau at the 9 month mark. You might also increase the number of times you offer the breast right now as well to help with calories. Sometimes babies at this age are distracted by all their new skills and aren’t asking to nurse or nursing as long as they need. We’re in it too— good luck and LMK if you would like to chat more about any of this! 
 

Give your LO time to explore and enjoy and trust that it will pick up as she’s ready! 
 

I would recommend getting a referral to Kaiser pediatric occupational therapy. Our son had difficulty transferring milk through breast feeding and we were referred to Kaiser pediatric physical therapy to evaluate him when he was a newborn for low muscle tone. They were great and gave us helpful exercises. We had to advocate many times with our pediatrician that we would like to be referred to occupational therapy in addition to physical therapy. We did get a referral to a Kaiser occupational feeding and speech therapist and she has been very helpful in guiding us to make sure our son is gaining strength he needs to feed more efficiently. Pumping, bottle feeding, and doing the OT exercises has resulted in him growing much more rapidly than before. I feel much more empowered with the resources we get through the occupational therapy appointments. I know that Kaiser's occupational therapists work with babies and kids of all ages and specialize in feeding issues.

Take the PT referral and you could call  the regional center. Likely no big deal but low tone can impact other development as well

So, first, I would ask your doctor for a referral to early intervention based on the low muscle tone thing.  This is a free state program for kids 0-3.  I haven't done it in California, but when we arranged it in CO they were incredibly helpful and offered to do stuff like pay for swim lessons.  (Then we moved and it seemed like a lot of hassle when our kid is just meeting milestones like 3-4 weeks late. But it really is an excellent program!)

Second, think about whether you're offering foods that are calorie-rich.  A lot of times people start with like, carrot puree, or cooked sweet potato, or other vegetables, and the foods just don't have much in the way of calories. Calorie dense foods: risotto with meat broth/parm/butter; avocado; oatmeal but with a lot of heavy cream or coconut milk; meat (my kid absolutely LOVES feeding herself little shreds of meat).  My kid also won't really take a spoon, but there are a lot of delicious high calorie foods that work for self-feeding.  

Third, think about whether you think your pediatrician is right.  I found this article about growth curves super helpful. Some kids just bounce around growth  charts and that's normal. Obviously your ped has more information than I do, but outdated ideas about growth do persist in all kinds of places.  https://www.nytimes.com/2020/04/17/parenting/growth-chart-accuracy.html

Just wanted to share a super helpful resource: https://solidstarts.com/

This has been my go to for all things baby feeding. They have lots of helpful webinar and blogs on picky eating, food refusal, you name it. I also follow them on instagram. 

Hope it helps!