Did you check your OS settings the Time Zone is correct and that your not using Proxy or VPN access?

My weather location shows Atlanta. I am home in NC. Will not allow me to change, I have entered my zip and also tried city and state, Nothing happens

It goes by your IP location however you can Report inaccurate location. https://support.mozilla.org/en-US/kb/get-your-local-weather-forecast-firefox-address-bar

had internet provider reset modem. before even amazon said I am from atlanta. the reset fixed all problems except weather location.

What program is doing the weather?

firefox top left hand corner

don't know why but problem corrected when I turned on computer today

Sounds like a OS or ISP issue finally fixed the location settings or Windows update fixed the location settings.??

What program is doing the weather?

https://support.mozilla.org/en-US/kb/customize-items-on-firefox-new-tab-page#w_weather

See also https://support.mozilla.org/en-US/kb/get-your-local-weather-forecast-firefox-address-bar