I think it has more weight to show you as an expert in a niche or when you own a software for promotion..., to get followers + discuss with them and to make contacts (as in Linkedin,...)

The number of +1 is considered as a ranking signal in Google. Sharing is caring.

It does carry weight SEO, after all it belongs to the search engine Google.

Simply put : Yes it does

Yes, google +1 have carry more weight for SEO.