Walt, it sounds like your default web browser is taking ownership of Weather Watcher Mobile’s internal browser. The only known workaround for that problem is to set IE as your default web browser.
I had the same problem (and same question). No, that’s not how it’s supposed to work – the weather data is supposed to be displayed in the blank space under the row of tabs.
I fixed it on my phone (AT&T HTC Fuze) using a fairly small registry tweak that only changes the default browser in a very limited set of cases (clicking on a link in an email, for instance, still goes to Opera, in my case, not PIE). If you’re comfortable editing the registry, click here for a description of what I did.