Your dragon looks perfectly fine and is not overweight at all. There's nothing wrong with her beard at all, they all get very large as they get older and larger, that's where their name comes from. My girl who is now a year and 2 months old has a beard that is at least 2 to 3 times the size of your dragon's beard, and yes, they're loose unless they are filled with food or water that they're storing, or unless they are puffing them up.
As far as the insect situation, usually at about a year old is the time when they start to switch themselves over from mostly live insects to mostly fresh greens/veggies. So you need to try to make her a nice, big, fresh salad every day, and try to make it up of a lot of different types of fresh greens and veggies. My girl went through this about 3 months ago, she used to eat an enormous amount of large BSFL every day and little to no salad at all, but about 3 months ago at 11 months old she just suddenly started refusing to eat nearly as many BSFL and started eating almost all of her salad. So I started to make her salads larger and more diversified, and she started eating more and more of it every day. And I still offer her live insect protein every single day, some days she'll eat a few BSFL, some days she'll eat no BSFL, and once in a while she'll eat a ton of BSFL, but she eats her fresh salad every day. The way I diversify their salads is by buying bags of mixed greens and mixed salads. Walmart sells a huge bag of fresh greens called "Country Greens" or "Greens Trio" that contains Collard Greens, Turnip Greens, and Mustard Greens, all 3 very good for Dragons. The bags are massive and only cost $2.98. Then I'll buy a couple bags of pre-made, fresh salads, the Thai ones contain all healthy greens and veggies, such as Bok Choy, a little Kale, pea pods, broccoli, carrots, etc., and they only cost $2.99 a piece. Then I'll buy a few different colors of Bell Peppers for $0.98 a piece, and I chop them up and mix everything up for her, and she loves it.
I would completely top feeding the mealworms and the Superworms, for a number of different reasons...First of all, mealworms have absolutely no nutritional value to Dragons at all, they are very high in fat, very low in protein, and the rest is all hard, chitlin shell, which Dragons have a very hard time properly digesting. Dragons who eat a lot of mealworms almost always end up with Fatty Liver Disease...Then the Superworms, which do contain some nutritional value and are high in protein and don't have quite as hard a shell, well they are still extremely high in fat, and can be fed to Dragons, but not as their "Staple" live feeder insect, they should only, at most, supplement their main staple insect, which should be either crickets, roaches (several species), BSFL, or Silkworms, all of which can be ordered very cheaply online in bulk.
Here's the problem the mealworms and the Superworms have caused: They are junkfood, consider them like you feeding him McDonalds every day. It's a very common problem that once you start feeding a Dragon mealworms at all, they start refusing the healthy insects. Superworms work the same way, except at least Superworms have some nutritional value. There is absolutely no good reason to feed a Bearded Dragon any mealworms at all, so I'd stop them completely. Then choose a new, healthy, staple insect, like BSFL, which they usually really like, and feed him them, along with only 1 large Superworm per day. He's just got to learn that he's not going to get the junkfood anymore and when he's hungry he has to eat some healthy insects and then he'll get a treat...