Adding weight reduces performance, and anything that reduces performance can cause oscillation. Reducing the PIDs and generally retuning the PIDs is what is needed to fix this.
Also, you might look into enabling and adjusting TPA. That changes the PIDs based on the throttle setting.
Jello in the camera is something you get with CMOS cameras and it is entirely caused by vibration. CMOS cameras capture one pixel at a time. If the camera moves sideways between the time of the top scan line and some scan lines in the middle of the image then you can imagine that a vertical line would not be captured as vertical. CCD cameras capture the whole image at the same time and do not have this issue, but if the camera is vibrating, the next whole image may be shifted, and the image after that could be shifted back. That results in blurry video.
Vibration can come from motors that are out of balance, bent shafts, bent prop adapters, out of balance props (either long way or short way), props not firmly centered on the shaft can be mis-centered, or prop blades not tracking in the same plane when viewed from the side.
Balance everything the very best you can and maybe try anti-vibration mounting for the camera. Some multicopters have an entire platform that is mounted with vibration dampeners. It is common to also firmly mount the flight battery to this platform because the extra mass reduces the platform vibrations even more.