Nope. C10 (8ft fleet) weight for 1971 is 3605 lbs, and the C20 is 386 lbs heavier.
Here's a source for you:
http://www.oldride.com/library/1971_chevrolet_c10.html
The perception that trucks are piggish, overweight brutes is only a result of the past two (maybe three) generations of American vehicles which, due to incessant government nannying, are increasingly heavy and plain huge. Ours, however, ain't that way.
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'68 Dodge Dart 270, 225, 904, 2.76--"Lucy"
1996 Gmc 1500 Z71, 350, 4l60e, 3.73s
1995 Jeep Wrangler Rio Grande 2.5, AX5, 4.10s
1989 Toyota Pickup 22re, auto, 3.73