If you have AK of spades and flop is QT3 with 2 of your suit then you should push all in. You have certainly got spades and jacks and possibly aces and/or kings as outs too. This gives you up to 18 outs and if called by QJ you will be a favourite.

If you have 67 of hearts and flop is KJ3 with 2 of your suit, you will probably have only the hearts as outs and also the possibility of facing a higher flush draw and drawing almost dead. This means you will probably have no more than 9 outs.

You should also consider size of pot and stacks. If the pot is $10 and your opponent has $10 left that means even if your opponent calls your all in your getting 2-1 on your money anyway so are getting correct odds to chase if he calls with better hand.

If your opponent has $50 and pot is $5. Is it really worth pushing all in where if you get called you are basiclaly getting 1-1 on your money.

If by weak you mean tight, then obviously it is better to make this move against tight players who are more likely to fold as this increases your chances of winning the pot there and then and compensates for the times you are called and miss your draw.