I once read that taxation in Outremer was considerably lighter than in the Byzantine Empire or Islamic states, so perhaps people could move to Outremer as a tax haven.
However from what I have read Outremer was probably already about 50% Christian, but these native Christians were marginalised by the Franks. An important factor I think was that Christians had been tolerated by the Muslim rulers of the levant but were forbidden to carry weapons and ride horses for centuries, so they were not much good as natural recruits for the Army. Therefore their marginalisation was continued under the Franks, who looked elsewhere for their armies and ended up with the independant military orders and itinerant adventurers to add to the troops bound to the king.
Perhaps instead the Franks would have done well to boost the native Christians by encouraging them to use arms and ride horses which would make them more recruitable. Perhaps the native Christians could be forged into a peasant militia between the foundation of the Kingdom and Hattin some 4 generations later.