Overpair on multiway dry flop

UTG+1 is a really good 24/20/3.8 and the caller is a loose passive fish 37/1.

Do you guys lead or check here? If you check then the action goes: UTG+1 bets $85 and the fish BTN calls, what do we do now?

$5/$10 No Limit Holdem
6 players
Converted at weaktight.com

Stacks:
UTG ($945.00)
UTG+1 ($1327.00)
CO ($950.00)
BTN ($2876.47)
Hero ($3034.50)
BB ($1074.00)

Pre-flop: ($15, 6 players) Hero is SB :tc: :td:
1 fold, UTG+1 raises to $35, 1 fold, BTN calls $35, Hero calls $30, 1 fold

Flop: :4s: :7d: :4c: ($115, 3 players)
Hero ($2999.5)?

I would check/call the UTG+1 raiser once but fold if he continues, check/call button lead at least twice and (maybe?) block bet river.

And I'd probably bet for value if it gets checked behind.