By adding extra weight, you have reduced the performance. There are many ways to increase or decrease performance.
Any time you reduce the performance, you need to reduce the PIDs. It will act a little more sluggishly, but that is the price you pay.
First save your current settings so you can get back to them if you want: File -> ExportUAV...
For an easy fix, I would go into Stabilization -> Expert Advanced -> Bank# and reduce all 9 inner loop PIDs by multiplying them by say 0.75 each. If it still oscillates do it again (so you reduced them twice). Or start back over with your saved settings each time and try a different reduction factor. Numbers between 0.5 and 0.9 would be good test points.
If you plan to fly sometimes with / without the extra camera, put one set of PIDs in one bank and the other set in a different bank and use your FMS to select which bank to use depending on whether you are carrying the camera. Or just always fly with the smaller PIDs. It will not oscillate in either case, but it will react a bit slower without the camera than it used to.