いい天気でした is better to show the past tense of いい天気です。For example, あの日はいい天気でした/だった(more casual) means it was nice weather at that day. You can also say "あの日は天気がよかった"。It is natural Japanese too. It means that the weather was fine at that day. We can't say よかった天気です。. いい/よい is adjective, and it can't be changed to the past tense.

いい天気でした and 天気がよかった are same and interchangeable. But you can't say よかった天気.