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Hi Pam, If you don't get a response from anyone on this site, you might try RAOGK (Random Acts of Genealogical Kindness) site. I see there are 3 ladies listed for Brazoria Co. who will do record lookups and tombstone photos, maybe one of them would do an obit lookup, also. Volunteers on that site are supposed to only charge for out of pocket expense, such as copies, film, etc.
If that doesn't work, try the public library in Lake Jacksonk see if they have back editions of the local newspaper, if not, they should know who does. If you can track down newspaper you might get someone to make a copy, probably for a fee, of the obit for you.