Might depend on the kind of weathering you plan, but if it is something that will be confined to the hull, like rust marks from scratches or marine creature buildup, then that is stuff I would do later.

For example, on a tank I might weather the road wheels individually to show random chipping or damage to the rubber, but wait until they are on the vehicle before applying dust effects or mud so that everything matches up in placement and color. Make sense?

I find it easier to work from the hull up. Weathering and assembled as I go, with a light wash to blend it all in. Just prevents breaking off all bits on a ship that stick up.

Another word of advice is to thoroughly examine every photo of the ship and class so that you can to identify weathering patterns. Think about the ships history and time period you're modelling. If it's not long after a refit, chances are it will have a fresh coat of paint. End of a patrol or after some heavy fighting, the ships going to look a bit more worn out. Warships are generally well looked after even in war, it is after all a very large and expensive piece of equipment. Cleaning and repainting also keeps idle crew occupied and busy.

It's easy to go mad with the rust streaks. Have done that myself a couple of times. Worst was my build of HMS Kelly in Mountbatten pink which I plastered the rust on. It looked horrible after standing back and looking at it. And then a little digging around indicated that the ship was recently repainted before her loss. So weathering would have been minimal expect for perhaps some staining from the anchor. You live and learn.

Some on the other hand got beat up very quickly. Cheaply made Flower-class Corvettes for example, tended to look like floating scrapyards at the end of every convoy duty!

uboat.net is a good place to start for basic histories and records for lots of allied and axis warships.

Hope it helps, all the best.