What dos " weather tight " mean ?

pretty much. wind and rain.

it keeps out the rain

Yes all very well tj, but he asked about weather tight, doh. Means that it is able to withstand wind, sun and rain.

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!
:-)

close fitting , and usually insulated, providing a complete barrier to all the elements. in some instances helping to maintain a temperature inside as well.