Your best hope for this to happen is for the Hapsburgs to managed to further centralize their rule over the Crown of Aragon during the 16th or 17th century. To simplify mattes greatly, Charles I (and V) made Castile the center of his Spanish Monarchy. All the New World possessions were part of the Crown of Castile, while Aragon, which included Sicily and Naples, were legally separate. As the seat of Habsburg power, Castile bore the brunt of the costs of the Spanish empire. It was more heavily taxed, and supplied the majority of the soldiers and sailors who fought for Philip II in the Old World and the New. However, with the increasingly crushing burdens came the almost exclusive rights to trade and settle in the New World, within the limits established by the Court.
While there were many Basques and Catalans who served in the New World, and Italians were well represented in the the monastic orders, the majority of New World settlers emigrated from the Crown of Castile. At the same time, the Crown of Aragon had in Europe at least the same population as Castile if you include Naples and Sicily. Just by granting the Crown of Aragon the same emigration privileges as Castile could probably double the number of emigrants to the New World. With the large expanse of land available, and the higher number of children than New World settlers tended to successfully raise, that would have a large effect on the population of Spanish America by the end of the 18th century.
My recommended POD is for Don Francisco Gómez de Sandoval, 1st Duke of Lerma, to have a much more successful "reign" as first minister starting in 1598. Perhaps he could be prompted by opposition of the Cortes of Aragon to abolish that body, and their Kingdom as a separate legal entity, and merge it with the crown of Castile, and then prevail in the civil conflict or war that would inevitability follow. Even a despotic and feudal-minded leader would tend to impose the same policies on all of his domains, so if this coup succeeded, I would expect greatly increased immigration to Spanish America to be a byproduct.
Any thoughts on the plausibility of the above scenario?