Bees winger Weston drilled home from the edge of the box to cancel out Kevin Betsy’s 27th minute opener for strugglers Wycombe
The Chairboys striker’s low-angled drive from 18 yards left Brentford keeper Wojciech Szczesny with no chance.
Thereafter there were few chances in a match hindered by heavy pitch conditions.
The Bees were almost the architects of their own downfall in the 73rd minutes when a defensive blunder gave Betsy an opening but he drilled into the side netting.
After Weston’s late leveller former Bee Matt Harrold almost pinched maximum points for the visitors with minutes remaining but Brentford substitute Sam Wood raced back to clear off the line and secure the draw.