If You have a Private Weather Station(PWS) and would like to have a good view over the data and, as an add on, also forecasts from Weather Underground (WU) this free software probably solves Your problem. Despite that the project is terminated the code is available and instructions is available at my other posts
Online weather data could be picked up from many different PWS solutions which should leave their online files at the weather WEB-server.
Weather34 is written in PHP so "any" web server, even a hosted(web hotel), should be able to run it.
The picture is taken from a project where a Davis Vantage Pro2 is the data source and software is running on a Raspberry Pi 3 with a Apache server and PHP installed.
Some code to start with
And the full installation