mr boo

Hi I have 1999 YP 125 scoot, which has a charging problem. If I charge the battery via mains charger then install on bike the electrics will all work and bike starts and runs fine. The battery will over the course of 2-3 days use run flat, quicker if I have the headlights on for any amount of time (makes night time rides interesting!) I was going to replace the alternator, however, I have now seen that there is also a rectifier which could be the problem. Are there any obvious signs to look for that would point to which part may be at fault? A friend of mine put the battery on a volt meter and it shows that there is a very small trickle charge coming through when engine is running and no lights are on, but once you switch anythin else on the meter goes up and down all over the shop! Hope someone can point me in the right direction. Cheers