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If you want to get a really accurate number, although not free, any speed shop that does race car tuning or preparation should have a nice set of scales that enable them to do corner balancing and stuff. Dunno what they would charge, but if you had a hookup, most race car enthusiasts/mechanics do side work on the weekends.
You can probably get it for free at some kind of truck weigh station, but they are meant to weigh stuff that is 5-10 times heavier than your car. Or more! Dunno how accurate they would be at only a ton.
Happy hunting!
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