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The specs in the FAQ section state that a 65 fastback weighs in at about 2600 pounds.....I'd go with a trailer that can take bout 3000 to be on the safe side.
I weighed my car recently (66 coupe) with 3 people (driver and 2 passengers), full tank of gas, no ps, no pb, no ac, and nothing in the trunk (no spare either) and a 289 aluminum intake manifold, stock iron heads, and exhaust manifolds (not the heavy iron stock ones) with a C4 (stock) and he said it weighed 3360 so eliminate 450 for the people (skinny teenagers done weigh much) and that's down to 2910 for the car.....