While I’m not entirely sire what you mean by “simple weather station”, the Ecowitt series of WiFi weather stations do not require any form of cloud connection.
One possibility would be to deploy the Ecowitt GW1000 gateway (interface and indoor temperature / pressure / humidity) along with a WH32 outdoor temperature and humidity sensor (or whatever other sensors you desire).
Configure the GW10000 to point at the ecowitt2mqtt broker and HA will have access to all of your local data. You can even make pretty graphs in your HA UI if you like (this is using Dwain’s Dashboard and mini-graph-card):
or use the data to drive automations.
I’m not sure if that is “simple” enough (or possibly too simple), but you certainly don’t need to have any data going to the Cloud with this approach.