You have many options. You can do PPI such as solimba or others which let user download other applications then yours. And you get money whenever user install other software.
Other is simple ads in your app, say every 10 min (or whentever) instead of weather display, change it to ad. And you can then create paid app which doesn't contain ads.
Just download any free app on ishit or spydroid, and see for yourself how they display ads.
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I guess you can have quite high conversion rate if you display ads geo located based weather display.