I haven't seen every singe bridge in the world, so I'm not happy calling this bridge-ferry-gondola hybrid the weirdest. But it's definitely top five, and makes me question (once again) the sanity of Wales.
The Newport Transporter Bridge is a relic of a time when mankind wanted to conquer nature, but didn't quite have the technology to do it. Thanks to a combination of fast tides, low banks and 100-year-old manufacturing techniques, building a normal bridge with a road wasn't feasible.
So, the transporter bridge has an elevated gantry, which holds up a platform that carries cars from side to side. A century ago, it was probably a great solution for carrying horses across an impassable river; today, it's a detour to a normal road bridge.