The analogy you draw is between "nice to meet you" and "I love you", but these are not similar sentences. For one, "(It was) nice to meet you" is passive voice; "I love you" is active voice.
- (It was) nice to meet you.
- (It was nice to meet) you, too.
In addition, "I love you" expresses deep feelings, while "nice to meet you" is just a polite phrase.
- I love you.
- I love you, too.
If you want to say "me, too", you can say that, although in some situations in may be interpreted as less sincere than saying "I love you, too." Also, it's probably not grammatically correct, but that's the accepted way of saying it.
For me, 'you too' means '[It is/was nice to meet] you too'. It's simply an abbreviation.
You could, in theory, use the same response to someone saying that they loved you, although I would be careful with this, and perhaps only say it in casual circumstances, such as saying goodbye to a friend.
e.g. 'Bye! Love you!'
Personally, if I told someone that I loved them, and their response was 'me too' or 'you too', I would be offended. It sounds very flippant and insincere. 'I love you too' is really the best response. Assuming it's true of course