Cupid is the minor god of falling in love. This is a big responsibility, and he wanted Psyche to love him not for his godly good-looks but for his love and dedication. Now, obviously that's weird because he fell in love with Psyche at first sight, but he's a god.
Also, I have heard that Cupid wanted to make sure that, for all Psyche's beauty, she wasn't vain or shallow. If she makes her love-decisions based on looks, not only would Cupid not have earned her love but she would have loved him for nothing other than how he looked. Cupid wanted something deeper and more loving than that.
I have also heard that Cupid was trying to keep it a secret from Aphrodite/Venus at the time (due to jealousy), so keeping things covert was of the utmost importance! Otherwise, who knows what kind of wrath would befall upon Psyche?
The Greeks had a thing about looking back. It was normally depicted as betrayal (RE: Eurydice and Orpheus).