I can be bothered by stuff. "Bothered" is not as strong a word. It's more general. It can apply to more situations. If I start to think I'm offended by something, I think to myself Hold it. You really mean that? Say what I mean, mean what I say: that's an important goal. I take it seriously. So I may start to heft the big "offended" word, but -- because I have not enough upper body strength (heh) -- I try to make sure I really mean to lift it. I measure my response, and usually the measurement comes out to "bothered" instead of "offended." And I can be bothered by stuff, without being offended by it.
My former editor Lukas Kendall once pointed out that he thought "hate" was overused -- "I hate broccoli, or I hate my brother because he changed the channel" -- and he said that to distinguish between that casual use of the word "hate" and a case where he genuinely hated something, which in that case was the movie Ransom. He then explained his hate for the basic concepts behind the movie, which deeply bothered him. He could explain it. (He explained it well, in fact.) "Hate": a smaller word, but more compact and heavy with meaning. I need to be better at only using *that* word when I mean it.
Maybe I'm oversensitive to the word "offended." Is that anything like this?
(Hey, any reason to re-run that.)