Bike dude should stick to polishing his rod
The 125 has an internal balance shaft - this is why, as a single cylinder bike, it's so smooth. This means that 'balancing' the engine would mean understanding both inter-relate. They operate as a 'matched set' (in simple terms).
Polishing the rod could be seen as a sign
There's nothing wrong with the stock rod or it's shape or form. It's actually very smooth (if a person really wants to think about it) and it's heat-treated. I've yet to see any kind of rod failure even after some very severe abuse (prolonged pre-ignition that burned a hole through the piston and heated the top of the rod to the extent that aluminum transferred into the steel - literally).
In all honesty, it's all bullshit concerns. There are only two things that may be of concern. The weight of the piston is one. If the piston/pin are much heavier or lighter then the balance will likely be off and you may well feel it. In fact, unless it's a very, very well done kit you probably should expect to feel some vibration.
Balancing the 125 is beyond my abilities and I can't think of anyone that could do it (off the top of my head). It would require understanding the relationship between the balancer and the rotating mass (crank, rod, piston) and then modifying both to suit. In short, if you change the weight of the rotating mass then a corresponding change should be made at the balance shaft. What I'm getting at is that the two can be seen as a 'matched set' from the factory. I have no idea how to address an issue like that.
Having said that, I don't think I would be concerned about it. I've driven the bike with some pretty interesting vibration and it's no big deal. I also don't know for a fact that it will vibrate or how much. My guess would be that if it was really bad then you'd hear about it on the 'net.
I looked into making custom pistons that were same weight as the OE piston but it went no-where as the high end manufacturers did not have blanks in our small size. One did, but they never replied. Otherwise you have to use billet and they're about $500 so that was not possible
I really would have liked to see a very well designed high-end piston for the bike with a compression bump. This is an aside but...
In the end I took some meat off the cylinder (shortened it) so that I came up with a perfect 11.6:1 CR and adjusted the squish to near perfection. What I found when I did this was that the OE piston machining left a bit to be desired. That's what got me on to making a proper piston in the first place.
Anyway, back to topic, the only other thing is the fact that the 150cc injector is actually too small for a 166 displacement. I don't think this will be an issue but where it could be an issue would be at prolonged WOT operation. At WOT the stock ECU goes open loop and therefore ignores the 02 sensor. This means that it is running on fixed pre-programmed settings specifically tailored for the 125cc engine and the 125cc injector. So I would suggest that it would tend to be lean at WOT - probably not a big deal unless you are on the freeway at WOT for a long period.
During 'normal' non-WOT operation the ECU will be operating in closed loop and this means that it will read the 02 sensor and adjust the AFR according to their specs. In short, it will compensate for both the increased displacement and the increased injector size by reading the 02 sensor.
All of these concerns are probably not a big deal. I would not let any of them worry me. Vibration, if present, if just the price of changing the piston assembly with a non-perfectly designed component. There's not much you can do about it and it may not be important at all. On the fueling side, that would only tend to present an issue with prolonged WOT so I would not be to concerned about that either. Cold start warm-up enrichment by the stock ECU would likely be considerably richer though. This is based on the assumption that the stock Honda ECU would not go closed loop util the engine reaches a certain temperature. Up to that point it probably just adds a pre-set amount of fuel.
I have no idea as to what kind of quality the piston is. It's probably fine but I'm just one of those people that, unless I design it myself, or have Wiesco or Carillo do it for me, meh
I'll move this post to the maintenance section so all the free-loading leeches don't see it