Silver has no weight any more, since like 4 years ago or something. Also, all silver is now shared between the different storages and characters, so you need not withdraw money from any storage any more. You can however put silver into the central market to not have to keep it on your character (and potentially mistakenly buy 3 billion health pots or something).

well then you need to do Magnus so you can open any bank from any other bank

 The only downside is to do a long, long chainquest to get it done.