When dealing with perspiration, sweat is both future and past tense of the verb with sweating being the present. In regards to all other uses other than human perspiration sweated is the correct past tense. However, sweated is used commonly enough that its considered acceptable outside of the academic code of grammar.
Thank you, professor. Would you please explain the tense, usage, and grammatical rules for the word “swear” in particular, as it pertains to sweating? Like, one is sometimes heard to be swearing because that fat chick sure did sweat a lot. Or: she was so sweaty I could hardly...(insert appropriate phrase as appropriate). “I swear I was swearing at how sweaty that big ole gal got!”