@mfarhan There isn’t a way to do it at the < multiplechoiceresponse > level in your example. It could only be applied at the < problem > level. So you’d have to break up your questions into two distinct blocks.
Once that is done, the weight can also be edited in the settings for the block, too:
It would have the effect that I think you want of giving different weights to problems in a quiz. The trade-off is that users have to click submit for each problem. This is more clicking, but there are some pedagogical benefits to giving users feedback right away if you are including feedback on those questions.