I don't have any specific experience with that bike aside from a short stint on an MX track, but most of the 125s I've ridden do not run particularly cleanly at small throttle openings. When they are tuned to run well (as a race bike, on the pipe) they usually are rich on tip in and will "four stroke" if you hold the engine there. If it bogs (the hollow waaahhhh sound) then it is probably going lean, which you really don't want.
I think the one I rode was an '06? It was a top end only kind of bike. No bottom end, so I kept it up on the pipe the whole time. It was also kind of worn out from being a race bike for 10 years, but even so it was a fun bike to ride.
Step one on an older bike for me is always to clean clean the carb out really well, check what jets and needle/needle position are, and set the float height. Also make sure the cap over the slide is actually sealed - if it leaks, it shows up like a vacuum leak and can cause some weird stuff. Check to make sure that the side isn't worn or scored - if it is, it can cause an inconsistent leak path around the slide. I always set them up with stock settings to start with for a baseline.
It's a 125 2 stroke - how does compression feel? If you pull the pipe and look at the piston skirt, how does that look? Pistons don't live long in these if ridden hard, and low compression can show up as carburetion problems.
Repacking the muffler may also change how it runs, so you may want to do that before doing any tuning. Also, make sure the pipe seals to the exhaust port properly and isn't leaking,
Once you know you've got a solid baseline, that specific part of carb operation is pilot jet, slide cutaway, air screw, and a little bit of the needle. If you make a change, ride a bit before changing again. 2 strokes can take a bit to clean out and don't always react quickly when you're tuning the bottom end. My suggestion would be to either go down half a step or step on the needle (clip position, raising the needle) or go in a quarter turn or half turn on the air screw and see what it does. Raising the needle may cause it to be too rich and start 4 stroking at part throttle/loading up though.
I would not suggest turning the idle speed up to mask the problem on a 2 stroke. The RM125 I rode was set up to not idle at all - you want as little air and as much vacuum (fuel/oil) getting sucked in on overrun as you can. A high idle can leave you with a dry engine if you're coasting, which is no good.