I'm not sure I understood your question "How is BW database size relevant with BPC environment size?"
Obviously BPC DB is part of BW DB, so having BPC increases BW DB size, but I doubt you were asking that.
I'd assume you asked if size of BW can affect BPC performance. If you asked that then yes,
size of BW can affect performance of BPC, but not significantly. For example, if with empty BW you need just 1 Node of HANA but with populated BW you need 2 HANA Nodes, then it can have some effect on performance. But I doubt that effect can be really measured.
BW is prerequisite for BPC NW, so you can install empty BW system, but it should be there.
Regards.