KK top set in deep 4bet pot facing river jam

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KK top set in deep 4bet pot facing river jam

Blinds: $0.08/$0.16 (6 Players) MP: $30.92 (Hero)
CO: $16.00
BN: $17.40
SB: $23.69
BB: $16.24
UTG: $14.78
Preflop ($0.24) Hero is MP with K K
UTG folds, Hero raises to $0.48, 2 folds, SB raises to $1.92, BB folds, Hero raises to $3.84, SB calls $1.92
Flop ($7.84) 6 4 K
SB checks, Hero bets $2.64, SB calls $2.64
Turn ($13.12) 6 4 K 7
SB checks, Hero bets $4.13, SB calls $4.13
River ($21.38) 6 4 K 7 T
SB bets $13.08 and is all in

Vill is 24/20 with 6% 3bet over 859 hands. Stats seem somewhat typical but I have him marked as a recreational, probably because he was sat with <100bb once or something. I don't have other reads.

I did not realise I was deep preflop, so question 1 is whether we should be going broke here preflop (assuming he jams it). I suck deepstacked so really not sure what the standards are.

I made some standard 1/3 pot down to the river and intended to jam but his donk really sucks. I'm not sure if my bet sizing is good while deep, especially when I realised afterwards that I actually gave him direct pot odds to chase any FDs he might have. But even so, I don't really get people's range for playing like this. If he's 3betting merged then maybe some TT,JJ,QQ, and AQ, KQ type hands? I can't imagine he'd call down with TT or shove them given that the diamond is a scarecard. But maybe if he overplays even 1 combo of TT, or makes even 1 stupid bluff, then I can't really fold it for the odds. Am I overthinking it? I think it's pretty well accepted that river donks in the micros aren't bluffs and we should fold if we don't have the nuts :D

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