What does " weather tight " mean ?

Will not leak liquids. As in "store the solution in a water tight container."

Also, a water tight alibi means undisputable.

Yes. It means "weather proof". Hardware stores sell weather proofing kits for home use, like on windows; but if a commercial building states it is weather tight it might mean that it is designed in a way to withstand severe weather: thunderstorms, hail, possibly with a severe weather shelter - with concrete walls to protect from tornado's. I am not sure as to what size or kind of building you are referring to, but it would have a way to protect those inside from environmental elements. Hope that helps! :-)

Yes all very well tj, but he asked about weather tight, doh.

Means that it is able to withstand wind, sun and rain.