It seems as if they're continuing with the idea of giving his powers a psychosomatic origin. When he didn't want to be Spiderman, as in the second movie, his powers waned. In this one, it seems as if they're using the black Venom Spidey suit as a visual reflection of Peter's moral corruption as he seeks revenge for his uncle's death.
Of course, in the first movie, it's used as a sort of joke. He has the hots for MJ, then he's bitten by a spider, then he starts shooting milky white webs around his room without any control. Gee, I wonder if that's a metaphor for something.