More mass means more inertia, which means you get more body roll and heave. To counter this, you need to compromise on your suspension design (essentially make it stiffer) to stop the thing flopping about.

There is some nuance here though: more mass does potentially give you options in lowering the centre of gravity which can certainly help. Putting the batteries in the lowest point is a smart design move from this point of view.

In general, I'm not saying you can't make a heavy car have a good ride quality, I'm saying you can make it ride well in spite of the extra mass it has to deal with. Adding more mass doesn't magically let you have a better ride quality.