I looked back on this hand and I think that I lost money by check raising the flop. Should I have bet smaller to keep these people around? I can't help but think that I lost someones stack by my flop play.

Party Poker No-Limit Hold'em, $ BB (8 handed)

saw flop|saw showdown

CO ($39.50)
Button ($58.75)
SB ($49.50)
BB ($34.30)
Hero ($60.25)
UTG+1 ($7.50)
MP1 ($73.80)
MP2 ($53.30)

Preflop: Hero is UTG with , . SB posts a blind of $0.25.
Hero calls $0.50, UTG+1 calls $0.50, MP1 calls $0.50, MP2 raises to $1, 1 fold, Button calls $1, 1 fold, BB calls $0.50, Hero calls $0.50, UTG+1 calls $0.50, MP1 calls $0.50.

Flop: ($6.25) , , (6 players)
BB checks, Hero checks, UTG+1 bets $2, MP1 calls $2, MP2 calls $2, Button calls $2, BB folds, Hero raises to $10, UTG+1 calls $4.50 (All-In), MP1 folds, MP2 folds, Button folds.

Turn: ($28.75) (2 players, 1 all-in)

River: ($28.75) (2 players, 1 all-in)

Final Pot: $28.75

Results in white below:
Hero has 7d 7c (full house, sevens full of eights).
UTG+1 has 9d 9h (two pair, nines and eights).
Outcome: Hero wins $28.75.

Underboats are a very specific hand to play. Rececntly I have been slowplaying a hand like this. I probably would have just called the flop. My reasons for this are as follows. You want someone to make the str8 or the flush. You are going to be ahead almost every time on this flop. The only way you are behind is 87 and you are pretty much going to go broke anyways. If someone has a 8 they are most likely not folding anyways so to say you are protecting your hand against someone drawing to a bigger boat is pretty much irrelavent. And my final thouugh is by slow playing this you can fold on the river is the board is double paired over your hand. By slow playing you really arent increasing your risks, someone that was going to draw out on you before with trips is still going to draw out on you but on the flip side you can get as much money as you can in the pot.