You're going to be a bit of a bore
Achieving new distances, times and tackling hills you once thought was impossible is exciting stuff... for you. They probably won't be as enthusiastic as you, but that's fine. They just don't understand. They probably have interests that you don't get. So warn them you're going to be a bit of a bore and if they can't muster a few enthusiastic head-nods, maybe get a blog, or a cat.
It's going to take up a fair bit of your time
Hopefully they have something that can occupy them for a few hours on a weekend anyway, like catching up with that programme that they love but you hate, doing their own sport, visiting their family (score: you get out of that now you're training) or, if your partner is a man, taking a long sit down in the toilet.
They will be required for holding bags
One of the main reasons for having a partner is so that they can come to races with you and hold your stuff, thus saving you from having to queue for the baggage lorry. See, and you thought that it was something to do with love and stuff. They should bring along a book, phone loaded with games or newspaper to entertain them depending on the length of the race. And also some snacks, for when you finish.
If the first three items in the list aren't making them do their happy dance, this one will: running regularly is going to make you happier, fitter and put you in a better mood. So they need to get on board, encourage you out for a run when you don't want to go, and not make unhelpful comments like 'you look a bit red and sweaty'. Teach them the phrase 'you look awesome' and ask them to use it liberally when you get back from a run.