First of all, It depends on how we define "formal". In my book, adding 요 to the end of the sentence is not formal, but simply polite. Adding 니다 to the end of the sentence is formal. And no, just at the end of the sentence.

As you know, korean has informal and formal korean. formal korean is called 존댓말 as well. 존댓말 is to do you always have to put 요 behind the word whenever you meet older than you or you meet someone at first. okay. As for your question : " It is really nice weather outside, want to join me?" If I translate korean into that english, you could say that "날씨가 너무 좋아요. 저랑 밖에 나가실래요?"

im not confident enough to my korean skill as i can answer for your question but korean formal is not that easy there are a many of kind of formal. if you want to say in formal, you must be put 요 but its not the end. i learned about -요,-세요,-시나요 do you like apple? = 사과 좋아해요?,사과 좋아하세요?,사과 좋아하시나요?(the most honorary term) i thought korean is really easy when i learn it the first time but its increasingly difficult learn more and more. recently im really confused i learned quite a lot korean but there are another grammar. how amazing. i got to know that english is imperfect language after learned korean. its really thorough. but korean is easier than chinese to me because i cant even begin to learn chinese.