I had a similar problem with my pink snapper.
They usually don't bask. Mine finally got so weak and skinny...I broke down, and took him to a vet.
( $185)
Turns out he was sick and I had to give hime shots.
They normally don't bask. Basking is a natural instinct they have to try to get themselves healthy . The vet said it can be a sign that something is wrong and the instinctually need to bask.
first try raising the temp.
This wil also increase his metabolism and may prompt him to eat more. One of the first things they do when sick is quit eating. This actually makes the problem worse because they get weaker. A larger snapper can go a really long time without eating and its no big deal. But not the small guys. The vet has me raise the temp to 92 for a while.
Also make a better cover so the air in the tank is warmer.
( not airtight....jut more warm and humid. ) he said warm water and cooler air can give their lungs a rough time if they are sick. (this is a good thing to do even for healthy guys )
I used plastic wrap on most of the tank. Left an open area at one end for fresh air. It raised the humidity in the tank right away. MAke sure he has a place to bask if he feels like it.
And check how he looks underneath. If he starts looking really drawn and skinny ...especially around the back legs...get him in to a vet.
OK having said that.......my pink skin snapper is just a really weaker...less agressive turtle. He doesn't eat as much..gets sick easier...and he always wants to bask. They all are sort of different.
You might not hav a problem at all.
I have a tank with (3) 3-year olds.
They are all healthy and good eaters. One is about 1/3 smaller than the other two.
I have a tank with (3) 4year olds and same thing...one is much smaller than the other two.
YOu might not have a problem at all.
ne of the things I do when I'm not sure is isolate the problem guy.
Raise the temp ( air and water ). They really are sensitive to water temp and how much they feel like eating. My really big guys will pretty much quit eating under 65 degrees....and they'll eat aton if it goes over 80-82. This also makes it easy to see if hes eating if hes the only guy in the tank . You're doing a good thing by weighing him. If he really starts to lose weight...then get hime in.
Good luck and let us know how its going
Mike