$8.80 KK UTG+1 vs UTG raise

Pacific No-Limit Hold'em Tournament, 15/30 Blinds (9 handed) - Pacific Converter Tool from http://poker-tools.flopturnriver.com/Hand-Converter.php

SB (t1,952)
BB (t1,427)
UTG (t2,217)
Hero (UTG+1) (t1,470)
MP1 (t1,247)
MP2 (t635)
MP3 (t2,147)
CO (t905)
Button (t1,500)

Hero's M: 32.67

Preflop: Hero is UTG+1 with K, K
UTG raises t90, Hero calls t90, 1 fold, MP2 calls t90, MP3 calls t90, CO calls t90, 3 folds

Flop: (t495) 5, 2, Q (5 players)
UTG bets t30, Hero raises t250, 1 fold, MP3 calls t250, 1 fold, UTG calls t220

Turn: (t1,245) 4 (3 players)
UTG bets t30, Hero raises t500, MP3 calls t500, 1 fold

River: (t2,275) Q (2 players)
Hero bets t630 (All-In), 1 fold

Total pot: t2,275

Results below:

UTG - VPIP: 50, PFR: 25, 3B: 13, AF: 1.3, Hands: 24
MP2 - VPIP: 40, PFR: 0, 3B: 0, AF: 1.0, Hands: 15
MP3 - VPIP: 43, PFR: 4, 3B: 5, AF: 1.8, Hands: 724
CO - VPIP: 61, PFR: 4, 3B: 0, AF: 2.3, Hands: 23

How could this have been played better?

My thoughts:

Preflop: Flat as I don't want to discourage action behind by 3B'ing UTG raise

Flop: Raising UTG min bet sizing is small on this relatively dry board. Maybe raise to 350 for value from flush draws, queens and smaller PP's?

Turn: Blank on the turn so again betting for value, bet sizing with intention of getting it in on the river

River: Hating any heart or Q on the river. Still shove as planned on turn?