If the mass came from handwaving and just increased the core's density, what would happen to the plates? If, over the course of 200 years the planet fluctuated from +50% to -50% gravity, would the plates contract and relax? Would there be more verticality where plates meet?
With increased gravity the motion of plate tectonics should speed up and slow down with decreased gravity.
The main driving force of plate tectonics is gravity. If a plate with oceanic lithosphere meets another plate, the dense oceanic lithosphere dives beneath the other plate and sinks into the mantle: this process is called subduction. The sinking oceanic lithosphere drags the rest of the tectonic plate: this is the main cause of plate motion.
The same source also suggests that is a factor in the motion of plate tectonics.
However, convection is also driving plate tectonics. When you heat up noodles in a pan of water, you create convection cells: noodles move upward in the middle of the pan where temperature is higher, and downward on the edges of the pan where the temperature is lower. Such convection cells exist inside the Earth’s mantle. One difference is that the mantle is not liquid; rather, the solid rocks are so hot that they can slowly flow. Hot, less dense rock material goes toward the crust whereas relatively denser, less hot material goes toward the core.
At certain times and places, hot, upflowing rock material in these convection cells weakens continental crust to create rifts and eventually new ocean basins. The East-African Rift, for instance, is the result of such a convection cell breaking up the African plate. Convection cells were responsible for the breaking up of supercontinents many times in Earth's history.
If increased gravity causes heating in the mantle due to increased compression, then the action of the convection cells could be increased over the two centuries. Possibly the mantle will cool, even slightly, as compression due to gravity decreases during the falling gravity phases.
Even during many centuries of increasing and decreasing gravity major geological effects won't be apparent, with the possible exception of increased seismic and earthquake activity, simply because geological change is such a slow process compared to human timescales.
I am no geologist at all, but I doubt 200 years is a significant time span on the geologic time scale. Over 200 years a plate would have moved between 1 and 10 meters. If you compare this to the extension of thousands of kilometers you see it is not even a few percent.
A change in the gravitational pull on that time scale would have its effects probably greatly damped by the intrinsic time scale of the mantle dynamics, which based on the above I feel its way greater than 200 years.
During the times of increased mass there would surely be more and greater landslide in limited areas on the surface, where the rocks are unstable. I don't envision other significant changes on plates.