To answer your question, I believe Michael enjoys the character as he brings some of his personality to it. I think he is such a doll. It's refreshing to see a "real" person.
Here are some links:
http://www.tvfanatic.com/2010/05/michael-weatherly-optimistic-about-ncis-return/
http://www.tvfanatic.com/2010/04/behind-the-scenes-with-the-cast-of-ncis/
The 2nd link is where Michael Weatherly says: "It may be why my wife doesn't like my character that much. Because I will jump right into character. I mean, I don't have any problem just going DiNozzo on people."
http://www.tvsquad.com/2010/05/10/nciss-michael-weatherly-talks-contracts-season-finales-and-m/
"Your character, Anthony DiNozzo, is very idiosyncratic. How much of that is the writers and how much of that is you? When we first started, [creator] Don Bellisario made sure that I brought myself to the character. We talked about 'Magnum, P.I.' and how Don really encouraged Tom Selleck to make use of his sense of humor, his playfulness, as opposed to a strict rendering of a hotshot private eye living in Hawaii. Bellisaro allowed me the same freedom and encouraged me the same way."
Personally for me, I love Tony DiNozzo. He is my kind of perfect.
In watching from season 1-7; he has matured, just not at the rate we want. I find him charming, sweet, good natured, and his sense of humor is the character's way of dealing with his job, and what I would want in a guy. He's also serious when he needs to be, meaning I'd feel safe with him if I were in danger. Take McGee and Gibbs...they have different outlets (McGee his writing; Gibbs his boats), Tony doesn't.
When it comes down to it, Tony gets the job done, Gibbs likes him and keeps him around
I think that's all that matters at the end of the day. We have one Gibbs, don't need another. Hope this helped 