The weeds would have to adapt to being burned alive. Maybe by building a more thicker and heat resistant "skin", but would have to do that without using all its energy to do so.

In a horrible future its an arm race of higher temp lasers against weeds, that results in scene of a burning field of crops, with robots tangled in weeds shooting erratically as the farmer hides in the cellar for their life. Skynet becomes self aware, and the only solution to weeding is to destroy humans who categorize things as weeds, but the AI has categorized humans as weeds. Global famine and war ravage the human race, all because we wanted to burn some weeds.