Bottom set gets shoved on deep

Villian raises fairly tight and is more on the passive side postflop, caught him only once bluffing where he insta bet pot with 44 on a 8926r board after I checked my TT to him twice.
Weak flop lead, trying to induce a raise to build the pot as soon as possible.

$1/$2 No Limit Holdem
4 players
Converted at weaktight.com

Stacks:
CO ($311.35)
BTN ($92.22)
SB ($58.75)
Hero ($405.40)

Pre-flop: ($3, 4 players) Hero is BB
CO raises to $7, BTN calls $7, 1 fold, Hero calls $5

Flop: ($22, 3 players)
Hero bets $12, CO calls $12, 1 fold

Turn: ($46, 2 players)
Hero bets $38, CO calls $38

River: ($122, 2 players)
Hero bets $65, CO goes all-in $254.35

If I were to ever fold a set I guess i might here. The question is would he play an over pair this way? What was his timing on the river shove?

this is a baddd board to do the small bet to induce... either check or bet 3/4

River is like a super easy fold

fold river. I would check/call it instead... really what does he have that would call river the way the hand was played other than a flush?

Guys, tell me if you disagree, but doesn't it suck ass to bet flop small here?

We bet, induce the raise, we 3bet, then what, our hand is face up?

I reckon we either bet hard or not at all.