Hello! Great question! Slightly is used as a more precise way of saying somewhat. For example, you would say you are "slightly" taller than your brother, but if you were just being general about it, you would say your are "somewhat" taller than your brother. Somewhat is also an informal way of saying it. Hope this helps!

The only difference I can think of is that somewhat probably should mean more of something than just slightly. Imagine it in percentages. Slightly might be just 51% greater (bigger, longer) than something but somewhat can be a lot less limited --it might mean something like 65% more of something, etc. somewhat seems to always suggest more of something than just slightly. He's slightly overweight. (Say by 5 pounds). He's somewhat overweight ( say by 20 pounds). That's kind of the difference.