chk my ranges on paired flop

[sarbox68]

vil is 31/23/1.2 over 36 hands... so basically anything beyond these stats is meaningless. He's 100% W$SD over 2 SDs (whoopee...), and I don't remember seeing either of them.

I should have 3b to 3.75-ish so fault #1. When he flats, I figure 77+, suited broadway, maybe some T9 or 89s stuff. I've never seen him 4-bet so no idea if he does or doesn't... so I'm leaving KK/QQ/AK in the mix.

The almost check-minraise on the flop narrows it down to 55 (maybe he does flat all pockets to set hunt v a HU 3bet...), AQ,KQ,QJ,KK, AA or QQ (only 1 combo of each, JJ-TT but weighted away from and maybe an aggro KJss or KTss kinda hand. And total crap bluff.

I get squashed by AQ,KQ,QJ,QQ but not a lot of combos of any of these 'cause of the board and my blockers. KK seems very possible as the full range of combos is still out. Throw in the JJ-TT and aggro draw possibility, and I'm not sure I can fold this.

So do I flat or shove? I shove to charge the draws / protect my overpair.

1. Is my range good?
2. PStove shows me as basically a coin flip vs. a TT+,AQs,KQs,QJs,AQo,KQoQJo range... of course w/ no weighting. With no reads other than those stats, and given what's in the pot, is the shove good?

Grabbed by Holdem Manager
NL Holdem $0.25(BB) Replayer
SB ($26.19)
Hero ($26.55)
UTG ($34.21)
UTG+1 ($25.13)
CO ($0)
BTN ($12.74)

Dealt to Hero AA

fold, fold, fold, SB raises to $1, Hero raises to $3, SB calls $2,

FLOP ($6) QQ5

check, Hero bets $4, SB raises to $10.50, Hero raises to $23.55 (AI), SB calls $12.69 (AI),

TURN ($52.38) QQ55

RIVER ($52.38) QQ55K

preflop is a good size since you're IP
you forgot 55
not so sure about JJ/TT either because those are the hands that possibly just flat