Two hands from weekend. I'm looking for criticism of my play and ranging, and what's my next action?

Hand 1
All players with about 75 BB. V1 didn't play a hand for several orbits and has shown down QQ, KK and AA. V2 likes Ax and will not fold even when told he is beat.

Me (UTG+1 with AA): raises to $17 (usual raise is $12 or less)

V1 (middle position): calls

V2 (big blind): calls

I think now is the time to construct ranges. V1 is 99+, and V2 is Ax or practically anything.

Flop ($47): KKJ

I think both players will not bet Kx -- we all check.

Turn: V2 bets $31

Me: ???


Hand 2
I have about $120. V1 has me covered and seems competent.

Two players limp, V1 raises to $10 from button.

Me (small blind with KK): raises to $31

All fold to V1 who calls with a sigh.

I think V1 is TT+/ AK, but AA and AK are unlikely.

Flop ($63): AJ6

Me: ???

Dude, hand 1, what card came off on the turn?

"I think both players will not bet Kx -- we all check." I don't understand how knowing that neither player will bet the nuts changes our decision. To me it would be great if we knew what they WOULD bet.

Hand 1, turn card was a 3 or 4. No flush draws either.

I didn't learn anything by checking the flop. Yes, if i knew they would bet the flop with trips, that would be great.

Hand 1--I cbet $25 and slow down on turn if one calls. AP.....it's a fold.

Hand2-- I'll cbet this again because of the sigh. $35 and again slowing down on turn if V calls.