Hi poker enthusiasts!

I've got a fresh hand, which I deem interesting b/c Hero faces a complete unknown Villain with a River bet.

Let's get into detail:

UTG: $17.14 (171 bb)
MP (Hero): $11.93 (119 bb)
CO: $16.42 (164 bb)
BU: $5.26 (53 bb)
SB: $10.00 (100 bb)
BB: $13.75 (138 bb)

Pre-Flop: ($0.15) Hero is MP with 3♦ 3♣
1 fold, Hero raises to $0.30, CO calls $0.30, 3 players fold

Flop: ($0.75) T♣ 2♣ K♠ (2 players)
Hero bets $0.36, CO calls $0.36

Turn: ($1.47) 6♥ (2 players)
Hero bets $0.80, CO calls $0.80

River: ($3.07) 8♥ (2 players)
Hero checks, CO bets $1.96
Hero???

I think the Flop bet is legit due b/c I often represent Top pair or second pair. Plus my hand has too much equity to fold to a float, b/c Villain can have anything.
Considering a "standard reg" range he often has Ax, middle pocket pair, some broadways (KQ, KJ and QJ especially) and also some flush draws.
Against many of these hands I have a nice Fold Equity. Also with half pot bet I just need to be successfull in only 1 in 3 cases. Plus I buy myself a Turn card to hit my set (asuming he calls in many cases) with high implied odds against Kx hands.

The Turn should not improve Villains a large portion of Villains hands and thus is no real threat to me. Given that many Turns are getting folded by Villains at the micro stakes I decide to Cbet again (high FE). Additionally my pot equity is still quite high and I bet higher to protect my hand.

The River can improve some hands from Villain (98ss, 97ss, pocket 8s). However this is only a quite small amound of his possible hands. I decide not to bet b/c there are no weaker hands that would call me (no reason for Value bet). I hope to get to the SD without calling a bet but if Villain bets, he could bet some missed draws (QJ, AJ, J9, 54ss, 75ss) and calling is a real option.

Betting 2/3 pot on this River from Villains standpoint only makes real sense with hands like AK, KT or a smaller two pair or a set OR with a bluff (capped betting range in my opinion).
If he puts me on AK, KQ, KJ he often check behind.
If he puts me on air, he does not have to bet If he hit anyhing or has a pocket pair.

What should Hero do?

Thank you in advance for your comments.

Greeting from good old Germany