Does a light rifle 'kick' more strongly than a heavy one?

ALL other things being equal (caliber, type of action, etc) a lighter rifle will have more recoil (kick) than a heavier one. It is a matter of action and reaction.

I have a heavy (11 lbs) benchrest target rifle in .308- it is a pleasure to shoot. I have another .308- a lightweight hunting rifle (6lbs). With the same cartridge, it will put tears in your eyes!