What evidence shows that white dwarfs must be very small?

Spectral analysis proposes that there is no hydrogen fusion roughly speaking. They are hot since they are very thick. So if you are a convinced high density and temperature and still not doing synthesis, you must be small. Also, stellar evolution models are founded on the observation of planetary nebulae, where stars have shed most of their mass after being red giants. The physics designates a small, hot, central remainder.