It is always a good idea to store the data somewhere external to have it secured in case of a system fault. In general the MB PRO stores your data locally and it allows you to do backups onto a USB stick.
However, when you upload to weather networks (like WU) they usually allow you to download uploaded data again in case you need it. I see this as a give-back feature for you providing your data.
You can also setup your own web page and store data there with one of the templates like HOMEWEATHERSTATION or METEOTEMPLATE or you can use subscription-based cloud services like Meteoplug.
So there are lots of options to choose from.