flopped trips vs lag

Villain is 37/15, AF of 1.15

Full Tilt No-Limit Hold'em, $0.50 BB (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

MP1 ($44.30)
MP2 ($49)
CO ($22.55)
Button ($50)
SB ($39.40)
BB ($10)
Hero ($52.50)
UTG+1 ($35)

Preflop: Hero is UTG with 7http://www.flopturnriver.com/phpBB2/...miles/club.gif, 6http://www.flopturnriver.com/phpBB2/...miles/club.gif. Hero posts a blind of $0.50.
UTG+1 calls $0.50, 2 folds, CO calls $0.50, 2 folds, Hero (poster) checks.

Flop: ($1.75) Ahttp://www.flopturnriver.com/phpBB2/...miles/club.gif, 7http://www.flopturnriver.com/phpBB2/...iles/spade.gif, 7http://www.flopturnriver.com/phpBB2/...iles/heart.gif (4 players)
Hero checks, UTG+1 checks, CO bets $1.5, Hero raises to $5, UTG+1 calls $5, CO folds.

Turn: ($13.25) 9http://www.flopturnriver.com/phpBB2/...iles/spade.gif (3 players)
Hero bets $14, UTG+1 calls $14.

River: ($41.25) 5http://www.flopturnriver.com/phpBB2/...es/diamond.gif (3 players)
Hero bets $15.5, UTG+1 calls $15.50 (All-In).

Final Pot: $72.25

I think the flop raise is actually too big. $3.5-$4 is fine.

I also bet much less on the turn. You run the risk of moving a bad Ace out of the pot.

If you raise the flop to $4, the pot will have $11 on the turn. Bet $8 on the turn, the pot has $27 on the river, bet $20-22 on the river or whatever he has left.

I usually lead out in these spots and expect an A to call me down, or c/c and lead the turn. I think the check raise gives them an easy fold if they have an ace with a meh kicker. I know I fold there. If he's really bad though, then your line is fine.

As you say, the c/r pretty well defines that I have at least a 7 in my hand here so with their call of it should we not be worried about something like A7, K7, 78 etc and slow down on the turn/river.

I don't like moving to c/c or c/f on the turn as that gives away the initiative to someone floating but with the passivity shown here by villain it may be a better way to go but won't maximize our value I guess.