I know I can be pretty obsessive about motorcycle weight (irritatingly so among my friends who ride "big bikes" who can't understand why I like flyweight bikes so much and won't ride bikes like they have anymore) but a vehicle's weight vs. it's power output is a very important factor in how well they perform, whether in outright performance or fuel efficiency.
I found a blog that uses basic math to show how much weight has on a vehicle's performance and wanted to share this with you:
How to Compare Weight Savings to Horsepower Gains | Tuner University
Like I said for me it's not so much about riding a 125 as it is enjoying a bike that you can throw around like a bicycle. If I could ride a 250 that weighed about the same as a currently available 125 like my K-Pipe (around 250# out the door) I'd be on it.