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Rashi says that Bilam said to Hashem בלק בן צפור וגו׳ – אף על פי שאיני חשוב בעיניך, חשוב אני בעיני המלכים.  Why would Bilam say something so ridiculous to Hashem, what is the חשיבות of being חשוב to a king against Hashem?  Rav Eliezer Lopian (son of Rav Eliyah cited in the back of Leb Eliyahu Shemos,) says we see from here the power of a bad middah.  It has such control over a person that it will make one do even foolish things so Bilam was led to say such foolishness because of his desire for honor and fame.
The footnote (not sure who wrote it) gives a different interpretation.  He bases it off an idea from Rav Leib Chasmon who asked what was the greatness of Shlomo that his wish was for a לב שומע, obviously a gift of great spiritual heights is much more important to request than riches and other physical benefits?  He explained that we see from here the pull of a person's middos, that even when talking with Hashem a person will still ask for physical benefits which are merely temporary. The person writing the footnote adds its not just that Shlomo asked for the right thing, that he asked the proper request.  The question Hashem asked was what does your heart really want, what is your true desire.  Shlomo answered that what was important to him was a לב שומע.  It was the fact that indeed it was his true desire that was indicative of a high level.  This is the peshat by Bilam as well.  Bilam didn't say I am חשוב to Balak but it was clear from his words what he felt.  The extra words בָּלָ֧ק בֶּן־צִפֹּ֛ר מֶ֥לֶךְ מוֹאָ֖ב give away what he was thinking, why the need to add the words מֶ֥לֶךְ מוֹאָ֖ב?  Because he was thinking about his כבוד.  That is what Rashi means, as he is speaking with Hashem, Bilam is still considered about his own כבוד.