3-handed atm. BTN folds and I open 9h 567ccc from my SB. BB calls.

Flop Tc 2c 4h.

My autopilot is telling me to c-bet 1/3rd here. But thinking on this hand I can't actually form too many good reasons as to why and I'd appreciate some feedback and discussion on what we want to be doing in these spots.

My main points of consideration at the time were this:
- I would c-bet here with most of my overpairs, flush draws, TPTK-ish and better type stuff. So this is in-line with my cbet range.
- 5 and 6 blockers reduce his 6 high straight continues.
- 9 reduces his Tx combos a bit

Some points I wish I could have considered in total, looking back on the hand:

• Having 3 diamonds reduces his flush draw range as well as his overall calling range. (cbet success more likely?)
• Bet/folding isn't a huge deal? Are we really throwing away that much viable equity with a bad FD/GS OOP? Only thing we feel comfortable on is the gutshot since I don't plan on playing for 100bbs with this low of a flush draw.
• No nut flush blockers and no actual made hand to protect, as well as it being single raised pot.
• Check/call puts me in a weird spot where I'm not even sure what I'm trying to make
• I don't have a lot of checkraise here as these players don't stab all that often.

Appreciate any feedback.