Does weightage on our performance in the essay depend on the stream that I wish to pursue? For example, if a student wishes to study Engineering or math, do they pay less attention to his/her essay score? (given that you don't need to be great at essay writing to be a good engineer) On the other hand, if someone wants to pursue a degree in History, does it mean that his/her essay score will be more carefully scrutinized?
It depends more on the type of college you're applying to than the major you've selected. If you're applying to engineering schools or conservatories then yes, you probably can get away with a lower essay score than if you were applying to a liberal arts school or big university; if you're applying to an honors program in the humanities, then you might be expected to have a higher essay score. However, most schools understand that the major you pick when you're a high school junior or senior won't necessarily be the major you end up graduating college with, so it's not necessarily a deal-breaker if you have a low SAT essay score but want to be a History major.