NL2, 6-max, KK vs dangerous board

Pacific Poker - $0.02 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

BTN: 126 BB (VPIP: 30.95, PFR: 19.51, 3Bet Preflop: 5.00, Hands: 43)
SB: 125 BB (VPIP: 50.00, PFR: 14.35, 3Bet Preflop: 6.25, Hands: 212)
Hero (BB): 100 BB
UTG: 100 BB (VPIP: 60.00, PFR: 20.00, 3Bet Preflop: 0.00, Hands: 15)
CO: 262 BB (VPIP: 32.43, PFR: 29.73, 3Bet Preflop: 22.22, Hands: 37)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K♦ K♠

fold, CO raises to 2.5 BB, fold, SB calls 2 BB, Hero raises to 7.5 BB, fold, SB calls 5 BB

Flop: (17.5 BB, 2 players) T♦ 5♦ 6♦
SB checks, Hero bets 8.5 BB, SB calls 8.5 BB

Turn: (34.5 BB, 2 players) J♠
SB checks, Hero checks

River: (34.5 BB, 2 players) 7♥
SB checks, Hero checks

Preflop: OOP, with KK, easy squeeze, IMO.
Flop: not so good flop. I have an overpair, while somebody could be sitting on a made flush or set, but also on TP or lower overpair. I bet to get value from the last two. If I were to face a made flush or a set, then so be it, but I thought the chances are slim.
Turn: bad card for my opponent. A T or 5-x, 6-x won't put more money, perhaps a ♦ would. I decided to check to pot control. If I were to be beat, I'd lose less.
River: another brick. The opponent checked twice, so he doesn't have much. Definitely not set or made flush, so I don't think a bet would get more value from weak hands.

I'd like to know your opinion.