K7 Flops Top Two Pair r River Shove over played

K♣ 7♣ vs A♣ 3♣

$0.05/$0.10 NLHE Hand Analysis

Hand Details:

UTG: $9.82 (98 bb)
CO: $15.31 (153 bb)
BTN: $9.66 (97 bb)
SB: $10.92 (109 bb)
Hero (BB): $9.82 (98 bb)
Pre-Flop Action
SB raises to $0.30.
Hero 3-bets to $0.95 with K♣ 7♣.
SB calls $0.65.
Pot: $1.90

Flop: K♦ 7♦ 3♣
SB checks.
Hero bets $0.63.
SB calls $0.63.
Pot: $3.16

Turn: 10♥
SB checks.
Hero bets $1.58.
SB calls $1.58.
Pot: $6.32

River: 3♥
SB leads out for $3.16.
Hero raises all-in for $10.36.
SB calls for $6.28, going all-in.
Showdown
Hero (BB): K♣ 7♣ (top two pair).
SB: A♣ 3♣ (trip 3's).
SB wins $25.20 with trip 3's.

Should I have bet larger on the flop or turn to protect my hand? Should I have Just called rather then go allin?