When the verb sweat refers literally to excreting perspiration through the pores, it is often uninflected in the past tense and as a participle. For example, it would be correct to write “I sweat through my shirt this morning” or “I have sweat through my shirt.” But to use sweated in place of sweat in instances like these is equally correct. Both forms are many centuries old, and they are about equally common in modern English.
Note, however, that some reference books recommend using the uninflected form, sweat, over sweated when you’re talking about perspiration. This advice is not borne out in real-world usage, but it means sweat is probably the safer choice if you’re writing for readers who are likely to consider dictionary-recommended forms the only correct ones.
When sweat bears any sense other than to excrete perspiration, sweated is more more widely accepted. For example, you could say that the pipes in the basement sweated, that you never sweated the small stuff, or that you have sweated bullets, and few people would question it.
Indeed, the crowd that sweated and danced at the Exhibition Hall wasn’t busy considering Gillis’ Jock Jams-ization of gangsta rap. [AV Club]
Egyptians and sub-Saharan Africans once sweated in these local bakeries as they churned out loaf after loaf. [BBC News]
He had sweated through the rim of his cap and the back of his shirt. [Los Angeles Times]