One of the many collocations in Japanese based on 気（き） 'attention', or 'focus', is 気（き）になる. This is just a combination of the noun 気（き）, に, and the う-Verb なる 'to become'. Also, 気になる will come after (A) が, where (A) marks the thing that is drawing the 'attention' or 'focus' of the speaker.
The most common translations for this structure are 'to be interested in (A)', or 'to be concerned about (A)'. This grammar pattern will appear before nouns, and noun-like phrases.
家（いえ）自体（じたい）は良（い）いと思（おも）うんですけど、やっぱり値段（ねだん）が気（き）になります。なんでこんなに安（やす）いんですか？
I think the house itself is nice, however I am concerned about the price. Why is it so cheap?
私（わたし）は高橋（たかはし）さんが気（き）になる。
I am interested in Takahashi-san.
やっぱりお前（まえ）がさっき言（い）ったことが気（き）になる。
I am still concerned about what you said earlier.
私（わたし）は好（す）きな人（ひと）の考（かんが）えていることが気（き）になる。
I am interested in what the person I like is thinking about.
Caution - Unlike 気（き）にする, which implies more that the speaker in intentionally putting their 'focus' on (A) due to it being difficult to ignore, the use of なる just highlights that (A) is 'becoming' something that is being focused on naturally, due to either the speakers concern or interest in the result.
私（わたし）が気（き）にすることは彼（かれ）が良（い）い人（ひと）かどうかだけです。
All I care about is whether he is a good person or not.
私（わたし）が気（き）になることは彼（かれ）が良（い）い人（ひと）かどうかだけです。
The only thing that I am concerned about is whether he is a good person or not.