To me, "cheesy" comes from cheesy grin, a sappy, overly sentimental smile for the camera.

Perhaps this meaning has been extended?

On the other hand, when I was in college (mid 1980's), we used cheesy as a contraction of cheap and sleazy. Our favorite phrase was: "Let's blow this cheesy joint."

Cheesy may also have assumed the connotation of chintzy.