First of all, stop handling him so much.
To a turtle, being held is stressful, and stress = lowered desire to eat AND a lowered immune system. Going back and forth from one place to another is stressful, too.
Second, see if you can get him something to hide in AND allow him more resting opportunities in the tank. Artificial silk plants from plant nurseries, dollar stores, or Wal-Mart can help with this. They're inexpensive and washable, and the turtles love to hide in them. You can also make a combination basking spot/cave by cutting out about a quarter to a third of the side of a small Gladware plastic container (from any grocery store). Leave the lid on, and put a small flat rock on top. The water can come up to the edge of the rock, and now the turtle can climb up to bask, or hide in the under water "cave".
Third, you mentioned a basking light and a heat light. Does your basking light not produce heat? What type of light is it? You need both a light that produces heat (which can be just a regular household lightbulb), and one that produces UVB.
Finally, you can add cuttle bone to the tank. It's the same thing used for birds. Just remove the hard back first, and break off a piece and let it float in the water. This will help him get extra calcium. But, unless he has a UVB light, or his food has vitamin D in it, the cuttle bone won't help much. If you live in a warmer part of the country, you could put him in a container outside UNDER SUPERVISION AT ALL TIMES for a few minutes each day, if the outside temperature is at least 70F. Something like a dish pan or small Rubbermaid or larger Gladware container works OK for this. He still needs to be in water with a place to bask, though.
Katrina