There was a Thomas Webb Baker, who was a NC State Senator from 1834-1840 from the 45th District (Burke-Yancy Counties). Is this the person you are referring to?
Dear Ms. Tunis,
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The information you are looking for in regards to NC State Representative Thomas Baker will be at the North Carolina State Archives. The NC State Archives website is: https://archives.ncdcr.gov/. Form that website, you should be able to find contact information for that repository.
We hope this is helpful. Best of luck with your research!
Looks like he was part of the Bakersville founder family. That's in Mitchell County, NC. There is a good history of his father David on the Mitchell County Historical Society will be your best bet on trying to track down a photo or more information. They have a great article about David Baker on their website here: https://mitchellnchistory.org/2019/06/30/david-baker-soldier-of-the-revolution-and-founder-of-bakersville/
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He is buried in North Carolina, there are 18 family member graves on the page.
There is a free website where you can find more information about him. It is familysearch.org...you just need to register to search.