Your issue is really a difference in lifestyles. When I was in sports in college, it was a challenge to convince my girlfriend that I needed to take the time to engage in training instead of spending it with her. I suspect that you have that issue as well - you don't want to give up your active lifestyle for a more sedentary life, and he sees no reason to become more active.
Your question, however has 2 different facets. You want him to be more active, and also end on "improving his health". The first can be fun; the second is (to me) more inclusive of not only activity but also diet, regular medical checkups, and other health-related things.
So let's focus on the activity side of things and assume that he doesn't have a reason for being sedentary (ie sleep apnea, depression, arthritis, or something else). We men are a pretty stubborn bunch. If we think something works for us, we stay with it. So nagging and driving him to be more active will be somewhat effective in the short term and on individual activities, but won't lead to more lasting changes. It will also badly effect your relationship. Really, you want to have him decide to do these with you and make it enjoyable for him.
The first thing I'd suggest doing is counterintuitive: let up a little bit. If you're not pushing as hard, most guys will tend to resist less. Yes, you care, but making him more resistant to change isn't doing what needs to be done. So take a step back.
The thing that my wife and I have done that has worked out well is to invite one another into our lives and do so gradually. She's making me into a soccer fan, a game she loves, by enjoying the games and encouraging me to watch for a few minutes. I watch, enjoy her company, and then move on after a few minutes. But the intervals are growing, and I have attended a couple games with her. Had she demanded I go with her, I would have but not enjoyed it. By her playing the long game, I was able to decide for myself to go with her and allowed myself to have a good time.
Keep in mind also that he's not in as good of shape as you. So a short walk for you may be pretty arduous for him. But again, invite him in. Take a 5-minute walk alone. Then invite him with - invite, don't demand. Or tell him you're going to the park for a short time. Or go to the back yard and kick the soccer ball around for a couple minutes. The key is for you to do something you enjoy, do it in bursts where he can feel like he's participated but not totally exhausted from it, and gradually work up as he gets in better shape.
Also, and this is important: do not make these activities into a big thing. That's a reason that I resisted doing some things initially - it was a big production to do something with her. In order to do something, we had to first do this, and then do that, and then after what seemed like an eternity of preparation we could finally do the thing we started out to do. I was worn out just from getting ready! So help him ease into it. For example: if it's a 5- minute walk, do you really need to do x, y, and then Z? Or can you just pick up and go? That has also helped the both of us become more active.
