The first answer to this sort of thing is to always talk with your advise who will know more about the state of the subfield than you will, and will definitely know the specifics more than people here.

However, that said, my general inclination is to say that things like this should be published. First, it is often the case that something that seems obvious to you is not as obvious as one might think otherwise. Our own ideas often seem more more obvious since we have been thinking about them a lot. Second, having extensions even small extensions can be useful for other people have as actual references. Third, at the vast majority of points in one's career you will not be hurt by publishing a mostly straightforward result, and that's especially the case if one is still doing one's PhD. Worse case scenario, you put it on the arxiv and then after sending it to a journal they reject it as too obvious.

That said, it is possible that the ideal place is not to publish it by itself, but possibly to publish it as part of some paper where one is proving larger results. But this again falls very much into a talk-to-your-adviser thing.

The first answer to this sort of thing is to always talk with your adviser who will know more about the state of the subfield than you will, and will definitely know the specifics more than people here.

However, that said, my general inclination is to say that things like this should be published. First, it is often the case that something that seems obvious to you is not as obvious as one might think otherwise. Our own ideas often seem more more obvious since we have been thinking about them a lot. Second, having extensions even small extensions can be useful for other people have as actual references. Third, at the vast majority of points in one's career you will not be hurt by publishing a mostly straightforward result, and that's especially the case if one is still doing one's PhD. Worse case scenario, you put it on the arxiv and then after sending it to a journal they reject it as too obvious. (And to echo Andy's comment below do not put it on the arxiv without consulting with your adviser.)

That said, it is possible that the ideal place is not to publish it by itself, but possibly to publish it as part of some paper where one is proving larger results. But this again falls very much into a talk-to-your-adviser thing.