It's not wrong to take care of ourselves and live a healthy lifestyle -- not at all. God gave our bodies to us, and He wants us to take care of them -- not just so we'll enjoy a longer life, but so we can serve Him more effectively.
But it's wrong to be so concerned about our health that it becomes an obsession and is all we think about. And this can happen to people of any age, not just older people. Why is it wrong? One reason is because constant worry can actually make our health worse. Stress and constant anxiety eventually take a toll on our bodies -- as modern science has confirmed. Job declared, "Fear and trembling seized me and made all my bones shake" (Job 4:14).
It's wrong too because it means we aren't trusting God for the future. It may even be an indication that we're worried about what will happen to us after we die, because we don't have any assurance of our salvation.
Urge your husband to put his life into Christ's hands, and to trust Him for the future. The Bible says, "Cast all your anxiety on him because he cares for you" (1 Peter 5:7). When we realize how much God loves us, our worries will begin to fade. In addition, encourage your husband to develop some new interests, such as volunteering to help others through your church or other organization.