Matthew Green scored from long range midway through the first half to make it one defeat in 17 league games for Torquay and move them up to second.
Green was unmarked 25 yards out and hit an unstoppable shot past Danny Knowles.
The hosts had made the better start and Scott Bevan denied Stuart Beavon, who later shot just past the post.
Weymouth were restricted to long-range shots after the break before Bevan was on hand to deny Pierre Joseph-Dubois in the 83rd minute.
Weymouth:
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Booked: Cutler.
Torquay: Bevan, Mansell, Woods, Hargreaves, Nicholson, Carlisle, Carayol (Stevens 86), Wroe, Hodges, Sills, Green (Benyon 83). Subs Not Used: Robertson, Adams, Thompson.
Goals: Green 24.
Att: 2,323.
Ref: S Creighton (Reading).
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