The phrase "Wait or weight broke the bridge" is a pun playing on the homophones wait and weight. It humorously suggests two causes for a bridge collapse:
In engineering, weight (load) is the real concern. Bridges are designed for dead load (self-weight), live load (traffic), and environmental loads (wind, seismic, thermal). Exceeding design limits—especially dynamic loads from crowds (e.g., 2000 Millennium Bridge sway) or heavy trucks—causes failure. "Wait" is the joke; "weight" is the physics.
The phrase may also reference the nursery rhyme "London Bridge Is Falling Down" ("Build it up with iron bars / Iron bars will bend and break...") or the game Bridge Builder where players test limits.