I realize I am probably flogging a dead horse at this point but...
Go to the [Meter_tmp] section and change:
LeftMouseUpAction=!Execute [
#WebBrowser# "
weather.com/weather/local/#Wea…"]
to:
LeftMouseUpAction="
weather.com/weather/local/#Wea…"
This will open the weather in your default browser (which from your question I assume is Firefox)
There is another LeftMouseUpAction in the [Meter_t] section but it doesn't interfere with the above changes.