Most waterproof watches are heavy and bulky because they need to withstand water pressure. They also rely on gaskets that are not particularly reliable.
An easier way to waterproof a watch is to fill it with liquid. Liquids are incompressible so there won’t be much pressure difference between the inside and the outside, and watch case and gaskets won’t have to withstand large pressure.
The liquid should be non-corrosive and non-conductive. For a cheap plastic digital watch without moving parts even extra virgin olive oil will work. A quartz watch requires something less viscous. The one shown in the picture was filled with Fluorinert FC-770. Left half of the picture is before, right half is after.
The process is relatively straightforward - disassemble the watch, submerge in liquid, make sure all air bubbles are gone, then reassemble the watch while still submerged.
It might be necessary to insert a small piece of closed-cell foam inside the watch case to help with changes in ambient air pressure. Plastic cases have enough flexibility, so this is not usually necessary.
One nice side effect is that watch hands and markers appear to be closer to glass surface when viewed at an angle.