I am afraid you are not the only one with this problem, this is global.
There is, to put it sinply, 2 to 3 times more Empire players than Republic players.
When my guild checked our assigned players it was around 2900 Empire to 950 Republic.
So just to let you know, you will not get any competitive numbers on Republic side on ANY server, unless some major guilds decide to re-roll factions.
You don't need equal numbers to have competitive PvP. It just means that the republic players will have access when and where they want. So basically most battles will be on their terms. Advantage anyone?