Well, your question asks what The Christian should pursue the goal of physical fitness with what aim?
Now, a Christian is a person, and it has the rights to work out, and make himself/herself look good, or feel good. Sometimes it brings honor to himself/herself. But I don't think that's the answer.
What is Christianity?
Christianity is a belief In Jesus and his teachings. Therefore, people who are Christians try to serve God in every way, no matter what they do, if they do it in the will of God.
The most applicable answer to this question would be to make himself/herself a more able servant of God.
Why?
Once you're a Christian, God will live in you, because he created you. He loves you.
If God lives in you, you need to take care of your body. Like said in his word. It is logical, though, if someone would want to come over to your house, you would want to clean it, and make it nice and fresh. Same here in your case, God lives in you and he wants to, therefore, if you pursue the goal of physical fitness, you will make yourself a more better servant of God, because you are doing his will by keeping your body in shape, because he created it.
Hope this helped!~ :D