I believe in this context it means "sufficiently", with the definition of sufficiency actually being defined by the person who asked the original question. In other words, the respondent is stating that he meets the questioner's expectation of liking girls.
Sadly, I can't think of another example at present. Sorry.
EDIT: Based on the conversation below, I revise my answer somewhat -- either conversant's views may be in use. However, the core point is still the same: it means "sufficiently".
"We've run out of beer! I'll just pop down the shop and get some"
"Don't bother, wine will be just fine" (implication: good enough for me)
You don't really like me, do you?
Rubbish! I like you just fine (implication: enough that you should be satisfied)