To pass successfully; survive.
To expose to the weather.
To go to the wind ward of.
Atmospheric conditions, as regards heat, cold, dampness, rain, winds, storms, etc.
The hot weather has come early, hasn't it? – The Ancient Law by Ellen Glasgow
We'll weather this all right. – A Voyage with Captain Dynamite by Charles Edward Rich
Am I to be only a fair- weather wife to you? – Nancy A Novel by Rhoda Broughton