As someone who is new in a position, you don't know your team well enough yet to know whether they have this perception or not. I'm not sure whether they've done anything that makes you feel this way, or if it's simply worry on your part that you could have done something wrong.
For yourself and those around you, the best thing that you can do is to stop worrying. Showing concern and respect for those around you is a good thing. You have to be careful that you don't overdo it. Without direct evidence to suggest otherwise, don't assume that you have.
If you have a mentor or someone on your team with whom you have built a relationship, you can discuss this with them. Let them know that you worry that your concern about your boss might have sounded inappropriate or as though you were trying to gain favor. Your trusted team member can give you some insight into how the team operates, whether you did inadvertently cross a line that made someone think you were trying to gain favor, and what you can do about it.
If you don't have a mentor like this, this is a topic that you can address with your manager. You'll have to do this very carefully, and in person. You could approach it as a general discussion of your communication style and that of the team. You can discuss that you feel like your communication style might be misinterpreted as trying to gain favor, and what you might be able to do to improve your communication style so that you don't sound like this. Part of your manager's job is to help you be the best you can at your job, which includes helping you understand how others see you and helping you improve in areas like communication so that you can be more effective in your job.
(Edited to remove the below text, since I misinterpreted a comment from the original poster.)
You say in the comments that he directly told you that this perception exists. It might be that someone has said something to him. It might be that he is uncomfortable discussing his health with you, and this is how he is framing the feedback to you. It doesn't really matter which is the case.
You should not discuss his health issues, either with him or with anyone else. When you have a meeting with him, you can offer a general, "how are you doing?" which is an innocuous greeting. Your manager can choose how much, or how little, he shares with you based. Don't ask others how he is doing, since you don't know if others have this perception. Continue to be friendly and open, just avoid topics that he (and possibly your co-workers) do not want to discuss.
The most important thing to do is to respect his wishes. If he does not want to discuss his health, that is his choice to make. Don't take this personally. Major health issues are difficult enough without having to explain the health issues to people all the time. You can be friendly and open without broaching this topic.