Hand 1:

Hero on button with KJhh. Villian competent player in the CO raises over one limp to 200 at 25/50. Hero calls and limper folds. Goes heads up to the flop. Flop comes J92 rainbow. Villian bets 250. Hero calls. Turn comes 10h. Hero has top pair, gutter ball and flush draw. Villian gets 400. Hero contemplates raising but just calls. River comes off suit 3. Villian checks. Hero? Should we bet to get values from worse Jack's or other pair and straight draw type hands if we bet thin. Or check behind as he can raise river to blow me off my hand. Thoughts?

Hand 2:

Hero in CO has A7s. Villian raises UTG to 600 at 100/200. Hero calls and goes heads up to the flop. Flop comes AQ9 rainbow. Villian bets 1500. Hero calls. Turn is A giving flush draw. Villian bets 2500. Hero calls. River comes offsuit K. Villian bets 5000. Hero?

Hand 1 - looks like vil has given up. Player depending, I'd bet if I was quite certain vil has no bluff raises. Looks like AK betting 2 streets and finally conceding. Betting in this situation is good because u don't show your hand and can therefore have a few bluffs on missed draws when this player double barrels then checks and u also missed. Checking doesn't give u that.

Hand 2 - stacks would be nice, but without much more, I think this is an easy call. Looks like u could b chopping anyway, and if I was the vil with AT I'd blast this river also, since it looks like u also have a weak ace and this is the only way to take the whole pot. He could have flopped 2pr but that is really all u are losing to. KK prob not in his range. QQ? Yeikes that would b bad luck. Need to know how deep u are tho to make better judgment. 5k if u have 50k behind is different than 5k with 12k behind.

These are my opinions, and I'm not a world champ. I learn as much from criticism of my own replies as I hope others do from mine.

hand 1:

I think that I am split between checking back and value betting, I think that should be around 50%, however, if a value bet is made; it should be around 30-35% to get called by a weaker hand.

hand 2:
The problem with calling with a hand like A7 here, is that a situation like this can unfold. On the flop it is a standard call, we flopped a pair, he has range advantage but we can easily call. On the turn, especially when the A comes, it decreases his Aces and makes us call again. However, and a big HOWEVER is, people will hardly ever bluff a second ace. this is really true, think about it from their perspective:
if he is bluffing he is representing the ace, if another rolls off, it decreases the number of aces he can have, on that ace turn, you are never ever folding a king/queen so not alot of fold equity for him. but a call is fine..

on the river however, I can't really find an excuse to call on the river, his betsizes increases on all Streets and his story makes sense. I think that he hardly ever has a hand weaker than AQ here, especially from an UTG starting position. I think its a standard sigh-fold.

thoughts?

Op doesn't say much about what kind of tournament this is. I think if it's a regular event, not a Sunday major or something like that, you just call. You are only losing to AK or AQ. Like I said in my reply, from the vil perspective, the only way to win the whole pot (without holding AK or AQ) is to bet and induce a fold. AJs & ATs could raise from ep, although you are correct it is unlikely. Some more history about the play would help here.