When I saw the term "weird", it made me think a little. Weird is usually used to describe something unusual outside the norm of society, right? The reason why I think you may have asked this was because it involved putting a product onto your lips, and that is usually associated with women putting on lip stick/gloss. Lip balm is mainly used for conditioning and moisturizing your lips. It is barely used for cosmetic purposes unless it specifically contains or gives off color, shine, etc. Even if it was a lip stick or lip balm, why shouldn't a guy be able to use it?
This is the part where people start to involve a second term: "okay". Is it weird? Is it okay?...for a guy to use lip balm. It is okay, and not weird at all for a guy to use lip balm.
Society may consider it weird for a guy to use lip stick or lip gloss, but it would still be classified as "okay". The reason why it may be considered weird is because the public isn't used to seeing men wearing make-up. The reason why it would be considered okay, is because there is no law or rules when it comes to make-up being applied to women only.
The flavored Carmex use flavoring which is a liquid, making the lip balm thinner and a little shinier. If you put too much on, it may be mistaken for lip gloss. If you are secure in yourself, you wouldn't let this bother you, regardless if people stare or question you about it.
In my opinion, it is not weird for guys to use make-up as much as girls do. I am an open minded person. Sorry for the long post >.> Your question sparked the LGBT advocacy side of me right out.