Well, if you install a lighter flywheel you reduce the engine's inertia, aka its ability to keep going even if you lift off the throttle pedal.
It makes the engine snappier and more responsive, but at a cost.
If you have a light enough flywheel (let's say below 4kg) and an additional load like an AC compressor or the generator suddenly requires more power from the engine because the AC kicked on or a high electrical load was switched on it can actually upset/lower the engines RPM enough to stall it.
That used to be pretty common knowledge, but all-motor tuning has gotten less and less popular so it makes sense for this kind of knowledge to get lost. No biggie.
My recommendation would be to either re-install a heavier flywheel (cheapest option), or to get a programmable ECU (expensive) where you can increase the IACV's duty cycle to compensate for the engine's lower inertia (Hondata lets you do that as an example).
Keep in mind that is only the culprit for your problems if your AC system is not faulty, but considering the fact that you compressor was recently changed and the system consequently recharged, leaks are most likely out of the question. (If the work was done by a competent mechanic)
That's because the system (should) be pressure-checked for a few minutes before they put the new gas/liquid in, so it should be leak-free.