$5/10 NLH 9-handed:

$1000.00 - UTG - Hero - AdQh
$2000.00 - Btn - TAG player it seems like. Late 20's full stack. Has raised a few hands to isolate the fish. Seems like a good thinking player

Preflop:
UTG raises to $35, Btn calls $35

Flop($80): 5d3c3s
UTG???

Part 1: Dividing this hand into 2 parts. First think about the flop decision. Villains btn calling range is probably approximately {22-QQ, AK, AQ, AJs, ATs, A9s, KQs-54s, KJs, KTs, QTs, possibly smaller Axs, but not of sure}. We are faced with either checking the flop or betting. If we check, it is a sticky spot because usually our range is capped at AK and we don't have enough info to be calling down too light from villain. If we bet AQ, then that means what hands to we check? Any? If we're always betting here and never checking, we're going to have way too much air in our range. I thought about potentially checking AA or KK here, but my problem with it is we don't know villain will bluff off, and we can get 3 streets of value from JJ-QQ, maybe TT. If we check and he bets, then we probably have to call because we are beating his K/Q/J high's and any Suited connectors he called with preflop that are 8/9/T high. We also have two over cards to some of his mid pocket pairs, so we're not drawing dead. But on a 2, would we call another street? Or just fold?

Part 2:

Flop($80): 5d3c3s
UTG checks, Btn checks

Turn($80): 7h
UTG checks, Btn bets $50

We don't have too much info at this point playing with villain, so I don't know if he is checking back a pocket pair here and going for 2 streets or if he checks back air, and is trying to get me off of A high. Or would he probably bet all his air on the flop. It seems very difficult to play the hand after we check and cap our range. But, if we are already betting hands like JTdd, QJss on the flop, do we never have anything to protect our checks? What should our range be for betting/c/c'ing (I don't know if anyone c/r's this board). Also, what should Hero do on turn?