Given how rapidly weed plants spread and grow, choking out all other plant life, how come after millions of years we haven't ended with forests full of thistle or pokeweed, as opposed to pines or oak trees?
A weed is just a plant where you do not want it. Totally a matter of context. Tumbleweeds are non-native, introduced centuries ago. I assume you mean the invasive species of plants that have been spread by humans and are disrupting ecologies throughout most of the world
Until recently, these plants we consider weeds were limited in their range to home environments simply by geographic barriers and surrounding unfriendly environments. And the natural consumers, parasites and competitors in the home environments had adjusted to these plants and kept them in check.
When non-native plants are introduced into a new environment by humans, most of them do not thrive, but occasionally a plant is wildly successful. Eventually the potential consumers, parasites and competitors in that new environment will adjust through evolution. But the tragedy is that many or most of the original species will be destroyed before that balance is restored in a new, way more simplified form. The landscape itself may be totally changed. Removal of a key original species can cause great change too: How Wolves Change Rivers.
Not only will many ecologies be reduced to much simpler versions, even if they eventually conquer the invasive plant, those simplified ecologies will closely resemble each other, if their geography is similar, even if on the other side of the world. If humans were to totally stop transplanting invasive species (collapse of civilization?), diversity would return after millions of years. We know this from Extinction Events.
So to answer you question, weeds before human intervention generally did not take over in their home environments because the potential weeds and their natural consumers, parasites and competitors all evolved together in a quasi-equilibrium. Now, however, most ecologies throughout the world are out of equilibrium because of environmental change and/or invasive species. This will inevitably lead to simplified, usually less robust, weedy ecologies throughout the world. That reduction in diversity might as well be considered a permanent situation compared to the timescale of civilization.