In the beginning of the series, Hibari always viewed Tsuna as one of the many "herbivores" in the world - weak unless in groups and useless. As the series progresses and Hibari finally begins to pay attention, he is able to see the strong sides of Tsuna. He has said that he doesn't understand the tenth Vongola heir - how he can be so weak yet so strong depending on the circumstances. He even says he would want to fight Tsuna when he is at full power.
Though Tsuna means little to him even in later chapters, he does develop some degree of respect for him. He begins to show up to fight for Tsuna voluntarily, though often giving the excuse of protecting Namimori's pride or something. In the Inheritance Ceremony Arc, when Tsuna loses his motivation and hope, it is Hibari, telling Tsuna to watch his fight closely, who reminds him what it is he is fighting for - his friends. He even goes so far as to say the sky (Tsuna) is what allows the clouds (Hibari) to do as they please. I think this is a good example from his own mouth of the respect that he has for Tsuna that he hardly shows. He does go on to say that he will one day "bite down" the sky, but I think it is more of a friendly rivalry (as friendly as Hibari's rivalries can get, anyway).
In the Future Arc, the Hibari Kyoya of tens year later seems to have accepted Tsuna as his "boss" and holds more respect for him than the current Hibari. He actively gatheres intelligence on Byakuran and co. and passes it on to those at the 10th Vongola base. He even voluntarily trains the younger Tsuna because he knows how much power is stored within him. Though he almost kills him in the process (Hibari does not fight casually) he has good intentions - helping Tsuna reach what he knows he can reach so that he can become the man Hibari has come to follow in his own way. It is revealed later in this Arc that it is TYL (ten years later) Tsuna, Irie Shoichi, and Hibari that brought the characters from the past into the future - a dedication to the tenth Vongola that the current Hibari does not yet have.