1. I love you as much as John does.
2. I love you much. John loves you much. Both of us love you so much.
3. I love you. John loves you as well.
We both love you. The degree or the amount of love is only the same. It doesn't mean that we love you so much.
-------------------------------
Does #1 mean #2? Or does #1 mean #3? What is the general meaning of #1?
I'd say 1, 2, and 3 mean the same thing, yes.
These sentences mean that both people love you equally (although I don't know how one can measure love!).