One effective way that I discovered for myself to solve WEAKEN questions is the following: you have to set your mind in a way that can come to the argument's conclusion even without the provided premise(s). Or you can have the premise(s) and still not come to the conclusion provided in the argument. This way you basically do not attack the premise nor do you attack the conclusion. You agree with both parts of the argument. However, you show that both the premise(s) and the conclusion can exist without one another, e.i. you reach the conclusion without the provided premise(s), maybe by providing the conclusion where it does not requiter premise or you have the premise(s) but the conclusion may not actually happen. So in the LSAT world's WEAKEN region the premise(s) that the argument provide do not guarantee the conclusion. That's how you "damage" the support. Below is an example:

Argument: Because Mike likes rich life he works hard to make money.

P: Because Mike likes rich life

C: he works hard to make money

One way is to show that P happens but C still does not happen.

(A) Mike likes rich life but that fact does not motivate him to work (I know its a simple argument but you get the point)

Another way is to show that C happens without P.

(B) Mike works hard since he enjoys his job (he does not work hard for the sake of money).

Please share your thoughts!

Thank you 7Sage!