Mr Kirkland,

First things first ; I definitely find "your man" on the rosters of Morgan's Texas Cavalry Regiment and Baylor's Regiment , Texas Cavalry, 2nd Regiment , Arizona Brigade. There is another A. Weathersby listed in the 11th Texas Cavalry. However, in the National Park Service System ( www.itd.nps.gov),a Ulysses A.D. Weathersby is listed on the first two Unit's rosters I mentioned. So , first of all, ( if you have not done so already)go to the website I just cited. You can find your man and his regiments. Yes, there may be a brief summary of these unit's histories . I did not look . However, all units do not have a history in the National Park Service System. Where there are unit histories, they are usually brief , 1-2 paragraphs.
But yes, there are other places where more detailed unit histories exist. Start with Dr Ken Jones wonderful website
www.tarleton.edu/~kjones/ . He is the head librarian at Tarleton State University ( Stephenville, TX) and he has developed a super web page for those of us chasing down our Texas and Alabamian Confederate ancestors.
When you get to Ken's website, scroll down to where you see the Texas in the Civil War ( or something like that) section and you will see that you have several functions to choose from. There is a unit history section and a unit bibliography section. That should either "light your fire" for further Texas Confederate research or resign yourself to the fact that you're really not that interested.
If your "fire gets lit" (like mine did a long time ago ) , then your fun journey has begun and there are plenty of us
at this Board and others like it that would be willing to point you in the right ( hope so , at least) direction.
By the way, of the three units it looks like "your man" may have served in, I find one book ( only a cursory look !!) that is in print that can provide you with some of the history of Morgan's outfit. " Between the Enemy and Texas: Parson's Texas Cavalry in the Civil War" , by Ms Anne J. Bailey. Barnes and Noble or the equivalent, may have it.
Good Hunting, Craig