Can ONYX withstand outside weathering

First I don't see how there could be such a thing as 'inside' weathering - if you think about it, it is not possible. The use of "outside" in your question implies that there would be an "inside" version of the process. you question would therefore have been better phrased " Can ONYX withstand weathering".

Onyx is a banded variety of chalcedony, a cryptocrystalline form of silica, composed of very fine inter growths of the minerals quartz and moganite. These minerals are hard and packed tightly together. This means that onyx will not weather very quickly and will be able to resist abrasion.