As a trainer who has seen several clients who came to me to start training “because my partner wants me to,” let me say that the first rule is not to try to FORCE them to start. While you may love your partner and intuitively KNOW that exercise would be good for them, nagging them into exercising, in my opinion, seldom works (at least over the long-term, which is what you want/need to help address health problems). It’s difficult to know (or at least think that you do 🙂 what’s best for a loved one, and then watch them NOT take that step or advice. However, self-motivation is the key to long-term habit creation.
My best advice? Help them by “leading by example.” Participate in healthy, daily exercise yourself. Eat healthy. Get proper amounts of sleep etc. Modeling the behavior you would like your partner to undertake is a great way to start. Then, give them the information that they need to LEARN proper healthy behaviors (Note: this does not mean to try to force it down their throat, but to simply give them the information that they will need). Last, ENCOURAGE them. Positive reinforcement in my opinion is a great motivator! When you see them do something to help improve their health (like exercise) give them some recognition or praise.
I hope that this helps. Good luck!