"Do you believe in love AT first sight?" The "at" indicates the first meeting of perhaps many. "...with first sight" simply sounds odd. If there was any logic to it, it would actually be this: "second sight" is another term for extrasensory perception. So logically "first sight" suggests our regular senses. Therefore... "do you believe in love WITH first sight" suggests that you normally need second sight to perceive love. *headache*

I believe in strong infatuation at first site. Love comes from knowing the person more deeply.

Yes I personal believe so.

No I don't, but I believe that people can be physically attracted to one another at first sight.

Yes, it would be proper to define "time" by using "with" first sight.