Congratulations on thinking for yourself. Against only one caller, betting would be correct, even then, you may believe yourself beaten, and play check fold, though betting shouldn't be incorrect. The overcards are as much scary for your opponent as they are for you. Maybe more so, because you raised.
Against 2, position would be important, though folding mightn't be wrong.
More than 2, forget it. Poker is littered with weak players who call with any Ace, or even any court card. Against this many, save your money.
Even though JJ is a made hand, once overcards fall, it really isn't necessarily top pair anymore, and therefore, can be regarded as a trash hand, believe it or not. Even KK can be regarded as trash under similar circumstances, ie, when an Ace falls on the flop, and you have opponents, particularly where they bet in to you.