He flew past his marker before crossing to Robert Dunn but home keeper William McCulloch bravely saved at the forward's feet.
In the sixth minute Weatherston had a short deflected after he broke forward from the centre circle and a minute later another run was only ended by an illegal tackle from Mark Cowan.
Stenhousemuir struggled to clear their lines from the free-kick and Dunn fired just over the bar. He then came close again with a glancing header in the 23rd minute as Queens remained on top.
Stenhousemuir however almost snatched the lead in the 32nd minute when Gareth Hutchison headed a David Templeton cross just over the bar.
In the main however the Spiders remained on top and they took a deserved lead in the 56th minute when Weatherston steered the ball past McCulloch after latching onto an Alan Trouten pass.
Queens continued to create the better chances and Weatherston and Michael Dunlop should have extended their lead. With nine minutes remaining the home side equalised when substitute John-Paul McBride shot home from the edge of the box and two minutes later the home side stole all three points when Stephen Canning turned a McBride cross into his own net.