Last night I was playing in a local home game. The table was 8 handed and started with a $50 buy in and .5/1 blinds, but it is really late in the night so 6 of the 8 people at the table are over $150 deep.
I have been getting horrible cards for a couple hours and have hardly been playing any hands, and I pick up K[s] K[c] in first or second position With about $110 in front of me. I open raise and make it $4 to go (people were generally open raising making it $5 or $6 to go, so it was probably a mistake not to go with the flow and make a standard 4x the BB raise). A $500 stack to my left calls as does the player after him (maybe around $200 in front of him) and the button (a little under $100). So we have about a $17 pot going into the flop, which comes down J[d] 10[s] 9[d]. This flop looks incredibly dangerous to me, but I still lead out for $10 because I have a strong overpair. In retrospect I should have lead out for closer to the pot, probably a $15 bet. I wanted to make a strong bet at the time, but I'm not very good at eyeballing the amount of chips that are just shoved into the middle and playing on the net certainly isn't good practice. Anyways, the $500 stack right behind me raises, making it $40 to go, and action folds back to me.

This player is someone who plays reasonably well, but too loose. He'll make a call if he thinks he is getting implied odds or pot odds, though sometimes his idea of having odds is a little warped. He has a tell on when he raises with a monster (such as A-A preflop) but he doesn't exibit this tell 100% of the time. He didn't show this tell when he made the raise, but I know that doesn't mean he doesn't have something.

I thought for a really long time but ended up folding here. At the time I was really concerned that he had something like a pair and a straight draw, 2 pair, or a set. I also thought he might make this move with something like 8-8 or Q-Q. A pair and a flush draw is a possibility. Before discussing the hand with a friend I didn't think to consider the fact that should me opponent have a pair and a straight draw it wouldn't be the usual coinflip against me because some of his outs were either not in the deck (because I had 2 kings) or made me a higher straight (if he had an 8 and was looking for a Q). In the end though, isn't this just a situation where if you commit your chips and get called you will either be dominated or not very far ahead? Isn't this exactly the kind of marginal situation where it is a mistake to back an overpair with your stack? Having raised $4 preflop and lead $10 into the flop I still had over $90 in front of me and have only commited about 10% of my stack thus far, so I think it is pretty easy to get away from this hand.

Was I playing this too weakly? Should I put my opponent to the test by pusing in another $50 and some change on top of his $40 raise? If he did have a strong draw He would almost have correct odds to call (and with the amount he had already invested it is probably a clear call) so I'm likely gettting called if I push unless he is on a stone cold bluff or maybe merely a flush draw with something like A-Xs.

I would fold but I would hate doing it. There are so many different hands he could have you have no way of knowing what card you need or dont want. Youre out of position to boot. If you hit a king, you might have him now with set over set, or he could just hit his straight if he has QJ...etc
Im betting he has a big hand and is ahead of you.

I think you hit the nail on the head in your post Bob, if he is a decent player he is not raising with nothing and there is very litte that he could be raising with that you are a huge advantage other than AJ. his raise pretty much pot commits you if you call or raise. A set ot two pair and you are in bad shape, a straight has you drawing even thinner. Even an open ended str8 draw or flush draw you are not a huge advantage. The only thing that he could be holding that really makes you happy is AJ. The fold is the right play unless you have a really solid read that you have him beat.