You’re sitting with 70+BB so ideally an open raise should be $110, but I’m fine with the $100 in this case as we must alter the so called “rules” to the situation.
The BB calls OOP with what is most likely a loose but fairly tight range (i.e. two paint, K-10+, or any pocket pair), albeit I know nothing about this player. The flop is actually really good for your hand, as something like KJ would be in real trouble here. You’re opponent over bets the pot. At this point I need to know more about you’re opponent and judging by stack sizes I would say we’re fairly early in the tournament and you don’t know that much about him yourself. However, over betting is something I generally consider to be weak, however, if he had a set of sevens or two-pair (J 10 would be my fear here) he would likely make this play as well –then again it’s not much of an over bet; this is the key junction of this hand, all further decisions will be based on this one.
Personally, I don’t think I’m putting him on spades here, but that’s not to say you’re not beat anyway.
I do have one nagging question that I must ask – if you thought he was on spades and the turn is a non-spade; why didn’t you shove the turn? The pot was ½ the stack you started the hand with?
If you were beat here it was two pair, not the flush, in my opinion – I think I call the river bet unless I think he has two-pair but am not concerned with the third spade; he could have KJ, AJ, or a busted straight really easily and unless you got extremely unlucky I think AA is good.