I am not a PVP type of guy, and I can see this being a huge issue. It effectively makes a world unplayable for one faction on a PVP server.
Several suggestions made good constructive sense.
I would also like BW to think outside the box and come up with some innovative measures to account for unbalanced play. Unbalanced factions will always happen, and when one faction is seen as owning another faction it will only get stronger. So mechanics must account for this.
Not being a programer I cannot tell you what is possible, but I will make a suggestion anyway.
Could there be a base multiplier applied to the smaller faction based on the current imbalance when fighting other players...not NPCs? So if Empire is up by 25 players Republic players HP and damage would increase by 2.5 or some worked out figure?
Maybe the smaller faction could simply be given an extra PVP only shield of strength ratio to population?
Hell, BW has smarter game designers than I could ever hope to be....if they try hard, and not rely on past game designs, they can fix the situation.