OOP with over pair/back door flush vs. retard fish

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Seat 1: DANKADONK ($51)
Seat 2: El Nino 1 ($129.15)
Seat 3: octospider1 ($18.05) -
Seat 4: Vladisl7 ($9.50) -
Seat 5: Hero ($81.65) -
Seat 6: Villain  ($65.90) ( I picked off a bluff recently with player. I checked 99 to a overcard board and he check called turn delay cbet. On very draw heavy paired board after floating me with Ace high 4 kicker bet river.  51/11/1.3 River aggression is 6 percent FCB 33 percent check raise turn percent is 33) 
Seat 7: Jeglodyte ($37.55)
Seat 8: Lupic ($50)
Seat 9: Bankir1987 ($8.50)


PRE-FLOP:

Vladisl7 posts small blind $0.25
Hero: posts BIG blind $0.50
Dealt To: Hero


Villain:($0.50)
FOLD Jeglodyte
FOLD Lupic
FOLD Bankir1987
FOLD DANKADONK
FOLD El Nino 1
CALL octospider1 ($0.50)
FOLD Vladisl7
RAISE Hero ($2.75)
CALL River_king_A ($2.25)
FOLD octospider1


FLOP:

Pot: $6.25
   

CHECK Hero (his range for limp calling open in EP is close to 50 percent. He FCB stat is 33 percent. What are you thinking here. Are you betting for value if he is never folding? I dont see the point of bluffing a player that is not going to fold. )
Villain ($3)
CALL Hero ($3) ( I elect to call since I have overs and back door outs)


TURN:

Pot: $12.25
     

CHECK Hero (This player loves to bluff and bet and I assume there could be an ace in his range/random draw/two pair type hands/air. Since his range is comprised of mostly weak holdings should we raise here and move him off those holdings? If we raise and he shoves are you snap calling? I just thought he is too stupid to realize we are chopping with an ace.)
BET Villain: ($8)

Hero? (My intial thought was to check jamn all in but that removes all his BS and we chop cause he is never folding an ace.  He would call a jam with a set and a turned FD/two pair and a Ace. So does that make this a check shove for you?)