Installing a 200A meter base for overhead service on a shed/workshop building. Could or should I use PVC 2" through roof eve to weather head? Will PVC be strong enough to support elec. Cable from pole?

NO, no, no!

For a mast service you MUST use rigid metal conduit.
In most cases, for a 200A service, 2" is fine. Some areas will require 2-1/2" minimum.