river play induce a bet or bet and risk folding ?

preflop: ok

flop: i don't like the c/r here, you're owning yourself against the better Ax type hands, all of which are in villains range, while he can't have many worse aces. if he has sg like KK or QQ he'll often bet 3 streets anyway, so you're not losing much by staying passive. also you are letting him barrel his air type hands. against some villains it's a good idea to c/r and hope for him to spew or call down super light, but without reads i still like to just call.

turn&river: if you decided to c/r flop, i'd bet turn and bet the river as well, hoping to get calls from Kx (i believe he'll always call with Kx, and rarely bet if you check to him, especially on this river), or lower pocket pairs
your check ended up being a genius play, bc he had the QJ and decided to bluff it, but there shouldn't be many combos in his range he would turn into a bluff.. okay QJs JTs if he 3bets those pre, and some random spade draws that decided not to raise the flop or turn. (also note that he might bluffraise you with these hands on the river, occasionally giving you 2BBs from his bluffs instead of the 1 we get by check calling)

btw 3betting QJo vs an UTG open is really really loose and you'd have to be a huge maniac for it to be a profitable 3bet for him.

First of all you should fold Preflop. The reason is that you're quite dominated against a button 3better and a BB capper. At least one guy will have AJ+ or a huge pocketpair and you are just down to 3 outs and if you hit a T one guy will have an overpair and in case you'll hit Ax you could be either well dominiated by AJ AQ AK and if they have JJ QQ KK they may decide to fold if you raise. Button seems to be kind of a nitty regular. Lets check your equity against his range and also you have to assume how many worse hands he's gonna be calling down.

Board: A♠7♠3♣
       Equity     Win     Tie
MP2    50.55%  44.36%   6.19% { TT+, ATs+, ATo+, KsQs, KsJs }
MP3    49.45%  43.26%   6.19% { ATs, ATo }

Assumed he's calling down with TT-KK and he's got KJ KQ you have just 50% Equity but consider the fact that he could be raising with his better hands, sometimes he's folding TT since he won't assume that you'll checkraise after i got capped preflop and you'll have a tough spot, facing a turnraise. So with kind of a weak hand like that you should just check/calldown. You could think about c/c c/c donk River and fold to a Raise but that's quite exploitable but having a read it's ok and most players usually don't turn a pocketpair into a bluff.

As played it makes absolutely no sense to checkraise. That means "oh, i'm ahead, i do raise/bet for value" but the river changes just nothing. If he just called with AJ AQ he'll just call the river as well but you give him the chance to check back his pocketpairs that he could pay off with for one more BB. You played that hand inconsequently.

Thanks a lot. I can certainly see what you mean and the math shows im bad ♦ <3 thumbs up for you guys. both of you.