I didn't understand the logic of the first scenes of Requiem for a Dream. If Harry needs money, why not force his timid mother into giving it to him? Why drag her TV across a mile and pawn it? Why doesn't his mother give him the money when she sees him dragging away her TV so she doesn't have to go through the usual rigmarole? After all, she has money which she gives to the owner of the pawn shop.
Because most likely she doesn't have the money (at that moment)
Sara and Harry are quite poor - I don't remember if her source of income is mentioned, but it is definitely a meager one - she is a widow, so maybe a partial pension from her husband? A some sort of benefit? In any case, it wouldn't be much, and quite probably partially paid in food stamps, which you can't exchange for drugs.
In other words, she doesn't have any cash on-hand that Harry could take, so he is forced to pawn the TV for it. Sara is able to get it back when she manages to get some money.