As far as extra burden goes, I don't see a huge difference between carrying a handgun, or carrying a can or two of bear spray.
A typical can of bear spray with 10-12 oz of net content, must weight about 16 oz with the can and all. A lot of spray carriers carry two cans. That's roughly two pounds.
Depending on what type of handgun one might choose, he could come in about the same overall, or even lighter.
I call that a wash.
