A funny, and instructive, anecdote, courtesy of Mark Lance (Georgetown):
A long time ago my colleague Terry Pinkard said that the actual function of words like "obviously" "clearly" etc was as a stand-in for "I have no argument for the following". Ever since I've told students that a good way to find an easy paper is to read one by a famous philosopher, find the sentence that begins with one of those words and challenge it. This has in fact yielded a good dozen published papers.
For this reason, I try to avoid 'obviously,' 'clearly,' and 'correctly.' The last, at least when I do break down and use it, is shorthand for "I could explain this more, but it's not worth the extra two sentences." It most typically occurs in a lit review. If it appears in the middle of an argument, that's a red flag.