They may not be minature adults, but they are smaller people, and that is what I think some people forget. Respect and courtesey are reserved for "adults" as though "children" are a separate speices.
And that's why I treat them with respect and courtesy as I would adults, but I won't baby-talk at length even to an infant, because it drives me insane and doesn't feel natural or even "right." I might cluck my tongue at my 2-month-old niece and nephew, I might sweeten my tone of voice a bit when I talk to them, but I tend to avoid the baby talk - "would ickle sweetums like some milkie?" - I just talk to them like I would to an adult person, because even if they're babies, they are
people, at least to me.
I think the excessive baby-talking, once a child is past a certain age (say, 3), shows a lack of respect for a child as a person in his/her own right, because it's condescending. I talk to my 4-year-old godson as I would to any regular person, because he IS a person, and while I may not pull out the 50-cent words to hold a conversation with him, we do have some good and interesting talks, without me having to "sweetie-pie" and "punkin" and "baby" him to death.
My mom saw no need to coddle me on a daily basis just because I was a toddler, although if I was sick or hurt or scared, she would baby me a little bit while she comforted me. When I was babied by other adults just by dint of being a small child, I'd stop them dead in their tracks - I'd put my hands on my hips, give them The Death Glare (which I was an expert at, even at the age of 3, I'm told), and declare, "I am not a baby - don't talk to me like one." I think it scared some people.