I'm not sure I'd want to keep up with 6,500+ emails on either an iPad or an iPhone, after all those are much less powerful CPUs than any Mac of the last five years. Not sure what's suggested in
Paddy's links (I'm too lazy to check them!
) but you might try using the Rebuild function in Mail. Another thing to do is to keep your messages on your own computer instead of iCloud. Of course, that means you'll not be able to access them with the iPad/iPhone when you'r mobile, and that may be a major requirement for you.
Finally, you might check your settings in Mail, the default is set to never delete anything! It won't take long to end up with thousands of messages that are of absolutely no value! If I haven't moved a Sent, Trashed or Junked message within a month of its arrival or creation, it's gone! Period. I certainly don't want it cluttering up my server space!