I hope my explanation is helpful, it may be more than you are looking for but it is good to know why things are as they are.

The servo's you are using is standard size, under light load they draw about 150 mA. If you hang a 6kg weight on a cable and attach it to the servo horn (about 1cm radius) then you are drawing about 500~800 mA. Since in your setup you don't quite have that much weight, what you have is an extended mass, because of inertia the mass will resist moving at the speed that the servo circuitry is setup for. So the servo struggles to draw more current to compensate. This slowing down and speeding up causes current surges and voltage drops. That is why you see the oscillation.

The hobby servos are rated for 4.8v to 6v (grandfathered since NiCd 1.2v/cell). At 6v it will move faster than at 4.8v (0.20s/60 deg compared to 0.16s/60deg). So seeing a slowing down compared to using higher voltage is to be expected.

What test equipment do you have? Oscilloscope? Multimeter? etc...? What country are you in? is it difficult to get 9v @ 3A for example? If it is difficult then Skimask is correct in using NiMh or NiCd, or maybe even sealed lead acid (alarm system battery usually 3~6A)

Nick