So your "6 weight" rod performs considerably "better" with an 8 weight line...

THAT PRETTY MUCH MAKES IT AN 8 WEIGHT ROD NOT A 6 WEIGHT

All rods can be cast with a few different line weights, with "modern" fast action rods usually handling heavier-than-rated lines very well. Slower action rods seemingly don't respond quite as well to overlining in my opinion.

So now you have an 8 weight rod with a 6 weight sticker on it, and you can still drop to a 6 weight line if you want a bit more delicacy or if you know you're going to be using just smaller flies.