Did I overplay this hand? Should I be thinking about getting in as many bets as possible here are or about the most effective way to cut in my opponents odds? Any other way to protect my hand better? Keep pot small on early streets and raise turn perhaps? A few hands like these per session and the winrate plummets...

I have [Ah] in MP. UTG+1 raises, I reraise, BB calls, UTG+1 caps, I call, BB calls.

Flop: [9h][Tc]. BB checks, UTG+1 bets, I raise, BB calls, UTG+1 reraises, I cap, both call. At this point I'm most worried about BB having something like 99.
UTG+1 most likely has JJ-AA; he wouldn't cap with a med pp or AK preflop.

Turn: . BB checks, UTG+1 checks, I bet, both call. Now I'm sure none of them has a set, so BB is on a draw and UTG+1 has JJ,QQ or AA (most likely he would have led out again with AA).

River: . BB leads, UTG+1 folds, I make crying call?? and lose to JTs.

If you're playing against a BB as loose as this, there's really not much you can do on a board this coordinated. I think you're pretty soundly beat here when he leads on the river, but I still call here unless the BB is very passive. If you had raised on the turn you might have gotten the BB to throw away his JTs, but as loose as he was previously, I doubt it. He's got second pair and an OESD, I doubt he's going to lay that down. That said, you can't put him on that hand on the flop. I probably play this exactly the same way, depending on my opponent. I figure by raising on the flop I have a pretty good chance to go ahead and drive out the BB instead of letting him draw another card. If he's passive, like this guy seems to be, I go ahead and get him out while I can.

It might also help to think about Sklansky here. If you knew what he had, would you still play it the same way? If he knew what you had, would he play any differently? Certainly preflop his call is bad. Postflop, though is a different matter. On the flop after the bet and raise he's getting 8-1 and he has an OESD and if he gets another T he's improving there too. So, if I was him and I knew you had AA, I'd call. If I was him I'd probably want you guys to cap the flop, too.

In the end though, it boils down to having to step carefully on a board this coordinated when multiple people see the flop. I still think if you protect your hand on the turn he's going to call you, but at least in the long run this call will be a bad one.