No sweat.
This simply means no problem. It comes from the fact that doing something is easy and won't cause you to sweat.
Jill: Can you help me fix my car?
Jack: Sure, no sweat. I'm good with cars.
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General: How did the mission go?
Soldier: No sweat. Everything went according to plan.
I'm sweating like a pig.
This is used when you want to say you're sweating like crazy or sweating a lot. It is very casual and kind of crude so it's usually used between close male friends.
Warren: Wow, it's 42C!
Dick: Yeah, I'm sweating like a pig.
Warren: Me too, let's go somewhere with air conditioning.
Dick: Good idea.
If you use this expression to talk about someone else it is HIGHLY NEGATIVE so be careful. In this situation men or women may use it.
Nancy: My new boss is always sweating like a pig.
Fiona: Eww... gross!
Enjoy the upcoming cooler weather~!
Phil