Phrases like "so sorry", "very sorry" are commonly seen, but "quite sorry" sounds odd to me. At first I thought it might be because "quite" doesn't usually go with words representing negative meanings. for example, "quite good" sounds common to me, yet "quite bad" somehow sounds off (maybe I would say "not quite good" instead). I know there's nothing grammatically wrong with "quite sorry", so I'ld like to know how others feel about the word "quite" going with words representing negative meanings. Thank you!
When you apologise to someone, you want it to be as sincere as possible.
"Very" and "so" are both words that make something more - "so cool", "very cool".
"quite" however, is a limiter. Compare "quite cool" to "cool", the object that is just "cool" is better than the object that is "quite cool".
In the same way, being "quite sorry" suggests you don't care much about the person you are apologising to.