Get blood tests for sure. If your vet doesn't suggest them, I suggest a different vet. Birds need blood tests as they hide symptoms really well. So, CBC and chem for sure, I would recommend chlamydia (psittacosis), giardia, PBFD, polyoma, and maybe a fecal and some other cultures, too (if it's not too much effort). Even though you've had him a while, it's good to know for sure that he's not carrying anything and/or just not symptomatic yet.
A good avian vet should be able to feel the keel of your birdie to see if he's too fat or too thin and they should do a range of motion type test on wings, feet, etc. And look in the mouth, check the eyes, nose, vent, etc. It's great you have the weight record- that will certainly help your vet. And ask about the PBFD vaccine that's coming out soon- I'm getting that ASAP! Hooray for one less thing to be worried about.