The GenWed site has free Texas Marriage Records for many Texas counties. From this Texas page, click on the name of the Texas county of interest. In this case, I clicked on Limestone County.
On the next page, to get to the free records, you’ll need to scroll down past all of the commercial search boxes and links until you get to a section that looks like this:
Note that the last two entries go to Ancestry.com, however the other links go to free online records.
It may take some digging – but you can use this site to find free marriage records.