I've got my suspicions about what is causing this, but I'll ask the experts to opine:
My Buddy 125 has about 6,500 miles on it. Engine starts and runs fine. When I twist the throttle, the bike starts to roll forward for a split second and then it suddenly lunges forward although something "catches." It occurs regardless of how long the bike has been running if I start from a full stop.
This behavior started late last year and I noticed that it's fairly pronounced as I was prepping it for the season today. It's not an engine lag. I'm pretty sure it's a transmission issue (worn rollers?)
...Operating with impunity in the legal gray area between bicycles and motorcycles....