I'm asking this in the context of 2NL which may mean that I'm overthinking this compared to the rest of the players.

When you're in position on an open-ended straight or nut flush draw and the villain(s) offer you a free card after the flop should you take it? Does it depend on whether it was a raised pot or a limped in pot?

Sure it may improve your hand for free, but its also advertising "I don't have anything and I sure hope this next card works out for me!".

How do pot-odds factor into this? I get a chance to win the pot for free when it is +EV for bets up to 31% chance to hit the open ended straight draw and 35% for the flush.

But if they are also drawing, I'm giving them a free chance as well, and their draws might be less likely to hit like say an inside straight draw.

I'm inclined to bet into this situation for two reasons. First they may think I've hit top pair or a set on the flop and second it might discourage them from trying their draw. In this case, how much should be bet?