KK overpair vs pot donk bet OTR

Prima, $0.10/$0.20 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $3.60 (18 bb)
BB: $18.87 (94.4 bb)
UTG: $21.61 (108.1 bb)
MP: $10.23 (51.2 bb)
CO: $23.01 (115.1 bb)
Hero (BTN): $20 (100 bb)

Preflop: Hero is BTN with K♦ K♠
2 folds, CO calls $0.20, Hero raises to $0.80, SB folds, BB calls $0.60, CO folds

Flop: ($1.90) 3♦ 2♥ T♣ (2 players)
BB checks, Hero bets $1.20, BB calls $1.20

Turn: ($4.30) 7♥ (2 players)
BB checks, Hero bets $2.90, BB calls $2.90

River: ($10.10) 5♥ (2 players)
BB bets $10.10, Hero?

Unknown villain.

I think preflop + flop + turn are ok bets for value?

OTR vs this weird pot sized donk? There are not many draws OTF, except 54/56 or something like A5s/A4s. Perhaps few comboinations of BDFD. Half of them hit and i don`t see unknown donking like that with one pair hand => fold without more info?