I'd never seen or heard this before until I recently watched a TV series and had to ask my wife to explain.
My initial guess was that it meant "I feel sorry for you" when in fact it means something like "I'm very sorry" (in the direction of the listener).
"I dislike you" which is I ...verb... you is correct English
But 我对不起你 seems like "I sorry you" which is I ...adjective... you which is incorrect English
So, have I got the wrong meaning of 对不起 (in this context), is there a verb meaning which I am missing or is this a sentence structure unique to Chinese?
Wiktionary has a listed under verb the following meanings:
To cause someone embarrassment; to screw someone over; to do something to a person that would demand an apology later on
But I don't think "I caused you embarrassment" or "I screwed you over" is a very adequate translation of 我很对不起你.