"Lesser" is a descriptive adjective. This means it gives information about the nouns. In this case, the description is "inferior":
"She plead guilty to the lesser charge of assault."
"Hockey is wildly popular in Canada, and to a lesser extent in the US."
"A lesser man would have kept that information to himself."
"Less", on the other hand, is a limiting adjective, which is a group of adjectives that "modify the nouns to which they are applied by restricting rather than describing or qualifying."
There is no "more" equivalent of "lesser", but as "lesser" means "inferior", a word with equivalent meaning is "superior".