You get to keep a copy of that post FOREVER. Tumblr is not like Twitter in that if OP deletes the original post, all the shared versions of the post will be deleted as well. This is how Tumblr still has posts from 100000 years ago circulating around.
You get to classify posts with your own tagging system. It makes finding things easier. Searching a blog using tags is also more reliable than searching with keywords.
You get to leave comments in the tags of the reblog! It’s handy when you wanna react to the post but are too shy to talk to OP and/or others in the reblog chain.
You get an archive/scrapbook of all the things you like, which you can then showcase with pretty custom themes.
You get to identify as part of a community. Among fandom blogs, fellow fans will know you’re one of them if you actually reblog things. Any outsider can leave a like, but it takes a fan or someone really interested in something to dare to reblog.
You get to make friends! People follow other people based on what their blog is like. If your blog is empty, then what’s the point of following you?
You give the impression that you care about what other people say, and it will make others look at you more nicely (empty blogs can be suspicious).
You are less likely to be blocked by artists/writers. (I’ve seen some posts from artists/writers saying that they’ll block spam likers.)
You are less likely to be mistaken as a bot or a creep (again, empty blogs are sus).
