That right there is why raising minimum is a bad choice. Why the hell would you fold to a reraise all-in after a min raise? There's only 1 hand where you would be clearing correctly folding to a reraise, and that's AA. You're only a 7:3 underdog against KK, and you have around 4:6 pot odds.

If nothing else, you need to at least raise 450 so you can call kings with the right odds if he pushes you all in.

But then of course, A-K is a hand where you really want to see all 5 cards. With so much money in the pot after raising 450, if you don't get an ace or a king on the flop you'd kick yourself for not going all in before the flop because now you have 6 outs, and you just barely don't have the odds to call an all-in and you're gonna be shortstacked with absolutely no respect for your raises from the table afterwards. Which may work out in your favor...but chances are it will not.

There's no advantage in position here. You have around 3-to-1 odds of getting an ace or a king on the turn or river, compared to 2.5-to-1 pot odds if he bets you all-in now. So you have to be 100% sure that you aren't gonna get an ace or a king on the flop, 100% sure that he'll call your all-in with a lower pair if an ace or king comes on the flop, and around 90% sure that he's not gonna stuff you all-in without a pair after the flop. That's just impossible.

So if you're going to fold if an ace or king doesn't come on the flop, then YOU are playing weak/tight.

Edit: I agree with curtains, it's an all-in and nothing else.