So, as the title says, you have a weakened jawa defending from an attack.
The defense result is 1 block + 1 evade, the question now is: can Take Cover be used before the effect of weaken, or by being weakened i have no evade to convert?

Weakened has been ruled by FFG to be considered a Mission Rule and therefore always resolved first (followed by attacker then defender). So there is not evade to convert.

5 minutes ago, Uninvited Guest said:

Weakened has been ruled by FFG to be considered a Mission Rule and therefore always resolved first (followed by attacker then defender). So there is not evade to convert.

I agree, but the point to discuss is this:
The text says: While defending, the Jawa can apply +1 block / -1 evade to the defense result. Could that be interpreted as the jawa gaining 1 free block even if he has no evades, and in that case he defends -1 evade like if he was weakened?
(i agree with your reply, but it's actually something worth a clarification)

@Uninvited Guest is right, but Take Cover can be still be used.

Take Cover applies +1 block and -1 evade to the defense results. You don't need to have an evade to choose it.

You're right; I should have reread the ability before answering. Thanks for catching me on that.

You can use Take Cover even if you roll a blank.