If we upvote someone’s comments then we trust them to be a better authority, so we should give them a greater weight in vote totals. So it seems straightforward that a weighted vote count is a better estimate of the quality of a comment.
The downside is that can create a feedback loop for a group of people with particular views. Having normal votes go from 1x to 3x over the course of so many thousands of karma seems like too small a change to make this happen. But the scaling of strong votes all the way up to 16x seems very excessive and risky to me.
Another downside is that it may encourage people to post stuff here that is better placed elsewhere, or left unsaid. I think that after switching to this system for a while, we should take a step back and see if there is too much crud on the forums.
I think the LW mods are considering features that will limit how many strong upvotes users can give out. I think the goal is for strong upvotes to look less like “karma totals get determined strictly by what forum veterans think” and more like “if you’re a particularly respected and established contributor, you get the privilege of occasionally getting to ‘promote/feature’ site content so that a lot more people see it, and getting to dish out occasional super-karma rewards”.