how can I stabilize this without completely ruining the aesthetic of the bench?
Assuming that you don't want to fasten it to the floor or install powerful magnets or a massive flywheel, you need to widen the bench's footprint. Often, the legs are splayed outward to accomplish that, but since your bench is already done you might prefer to add a piece under the legs at each end, as in this bench:
You could use the same kind of wood that you used in the bench so that the feet are clearly part of the bench, or you could paint the feet to match the floor, or use a dark or neutral color so that the bench looks separate from the feet. Also, you could use steel plates instead of wood to minimize the change in height and add some weight at the bottom. Experiment with plywood or MDF first to determine how wide the feet need to be in order to achieve the level of stability you want.