NL10 - MP with 99

This hand pretty much plays itself, but instead of raising to $6.20, Should I should just push? I'm afraid that looks too strong and will scare weaker hands off?
My Re-raise was also too small here, should be making it $2, thus making villains 3Bet allow to to get my stack in?

CO: $10.72 (107.2 bb)
BTN: $9.36 (93.6 bb)
SB: $10 (100 bb)
BB: $15.55 (155.5 bb)
UTG: $9.85 (98.5 bb)
Hero (MP): $10 (100 bb)

Preflop: Hero is MP with 9 9
UTG raises to $0.30, Hero calls $0.30, 4 folds

Flop: ($0.75) 4 7 9 (2 players)
UTG bets $0.50, Hero raises to $1.40, UTG raises to $2.70, Hero raises to $6.20, UTG raises to $9.55 and is all-in, Hero calls $3.35

Turn: ($19.85) 8 (2 players, 1 is all-in)
River: ($19.85) 8 (2 players, 1 is all-in)

Results: $19.85 pot ($0.89 rake)