In the instance of using a GW2000 and a WH40, you would configure the GW2000 gateway to send the data to weather services like ecowitt.net and Wunderground at set intervals. Others are available although I have not used any beyond ecowitt.net (and ambientweather.net for my Ambient Weather equipment). There may be limits on how frequent the services accept data and on how much data they store. You can access your ecowitt.net data via their API:
https://api.ecowitt.net/Unfortunately it doesn't look like you can see any of the public ecowitt.net weather stations without registering for an account. If you did register, you can look at the map and see what the dashboards look like.
If you're wanting to look at the data, log/store it locally, and graph it, you can use something like WeeWX or even create your own logging and database system. There are other options, too, I'm just personally not familiar with their capabilities.