weewx can most certainly be set up to receive data from anyplace you can get data from, in whatever format it's in - IF you write the custom extension that does the work of course. Lots of people do things like read outside-generated flat files, CSV files, JSON, etc. Poke around the weewx-users google group archives for many examples.
FWIW, when/if you do this, 'definitely' put your second source of data into its own separate database. You can make the schema anything you want then and then cook up the right Cheetah template skin files to present it any way you want in the resulting HTML for your site. Works great.