What is Strahd von Zarovich’s weight in bat form?

This question concerns D&D 5e. The relevant ability, with my emphasis, is as follows:

While in bat or wolf form, Strahd can’t speak. In bat form, his walking speed is 5 feet, and he has a flying speed of 30 feet. In wolf form, his walking speed is 40 feet. His statistics, other than his size and speed, are unchanged… (Curse of Strahd page 240)

Simply put, what does Strahd weigh as a bat? Since size and weight are not the same, I would argue that he simply becomes a (very heavy) Strahd-weighted bat. Is this correct?