[Albert Moulton]

Fold or raise preflop to $.4 or $.5.

Then, if you get a caller or two, you can bet this flop because you have initiative, an OESD, and villain could have easily missed this low flop so you have lots of fold equity.

If called on the flop, then bet the turn or c/c or c/f the turn based on how much fold equity you think you still have vs villain's likely hand range. I suspect, in this case, a second barrel semi-bluff might be good.

Along the way, if villain comes over the top on the flop or turn, then you need to do some pot odds to see if you call or fold.

Now THAT would be playing your suited connector aggressively.

In the OP, you limp/call with a hand that is probably not the best preflop. So now you have no initiative, you are OOP, and you are heads up (all bad). Then you check/call the flop representing a draw - which is exactly what you have. So, while it is true that villain probably puts you on a flush draw more than an OESD, you are basically announcing what you have - which is never very good. A nice big c/r would be better than c/c. Or even a donk bet for the pot to see if villain gives up his AK/AQ might be good too. I don't like c/c at all.

Then you check the river, giving villain a chance to check behind. Checking the river is only good if you suspect villain has a missed flush draw here pretty often. Otherwise, he's not folding AA/KK/QQ/JJ/TT for $6.55 more. So, now that you made your straight, I'd push the river to represent a missed flush draw desparately trying to buy the pot. All those overpairs call your bet who might otherwise check behind on the river.