I know grandfather is Abuelo, but are there more affectionate terms?
In general, using the diminutive form of words in Latin American Spanish context is considered a form of affectionate variation. The specific reason, as per my understanding, is that "smaller" things (like little dogs, etc.) tend to inspire protective instincts, as well as a sense of "cuteness".
The same applies to Abuelo; by saying "Abuelito" you are conveying a more affectionate tone to it.
Another variation I've heard is using the word "Papito" along with your grandpa's name (like, for example, Papito Juan). This conveys the meaning that, being your father's father, you also consider your grandpa your "papi" (from padre, which is masculine form of parent).
This one I've noticed is common along those cases where your father and grandfather have the same name, as to avoid confusion when calling or talking to them. That way, you can affectionate refer to both as, i.e.: "Papito Juan" and "Papi Juan", for your grandfather and father, respectively.