Hayzee is a Crazee Dayzee with green petals (as opposed to the regular Crazee Dayzees, who have yellow or pink petals), whom Luigi met while on his quest to assemble the Marvelous Compass, during Paper Mario: The Thousand-Year Door.
Hayzee apparently lived in Jazzafrazz Town, where he wrote a musical entitled "The Mystery of The Fiery Hat of Social Awareness" for the annual Jazzafrazz Town Drama Slam. As it turned out, the compass piece that Luigi needed was a part of the Dramalama Plaque, the prize for winning the Drama Slam. So, Luigi became an actor in Hayzee's play. While Hayzee played the part of The Red Miracle, Luigi (much to his discontent) played the part of grass.
In the end, their music was the most popular by far, and they won the Drama Slam. As part of the deal, Hayzee joined Luigi on his quest. Hayzee tells Mario that after he and Luigi finish their quest, he wants to take his play all over the world. "Of course, Luigi will be grass"
Out of all Luigi's partners, Hayzee seems to be the only one that does not despise or find something wrong with him (with the possible exception of Screamy, as his relationship with Luigi is unknown).