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You didn't post up your location, so not gonna help you too much. Call around to places that sell rocks, mulch and other bulk landscaping material. They always have scales and some are not too steep. Ask nicely (and in person) when they are not busy and they might let you get weighed.
Can also contact an area SCCA or other group and see if a member has car scales to weigh your car as they sometimes try to get balanced weight for road courses/autocross and rely on scales to assist.
I weighed my car at the dump in VA Beach and I told the guy that comes out to see what you got that I just wanted to weigh my car and he didn't give a shit and let me go!