If one looks at the Spanish period, Texas was at the ass end of civilization. In the 18th century, the Apache played hell on the Spanish interest in expanding their presidio and mission system.
From 1821 to 1836 30,000 Anglo-Europeans immigrated to Texas, and at least half of that came in after Mexico restricted immigration in 1830. The problem is that Texas was still the ass end of civilization, and the Comanche had supplanted the Apache. They had rightly earned the title "Lords of the Plains."
The economy of the republic of Texas was a bit of a basket case, and accumulated 10 million dollars in debt in just a single decade.
But let's look at the numbers, between 1836 and 1850, Texas grew by more than 10,000 people per year. This was at a time when the ports were not much to speak of and you had to really want to get there to go overland.