Although I realise a behavioural explanation might hurt long established anthropocentric viewpoints, I believe the answer to this question is better understood if one adopts an ethological viewpoint.

In [ethology](http://en.wikipedia.org/wiki/Ethology) one describes tenderness as a way of consolidating mating bonding. It is indeed a well documented pattern in many evolved animal species that individuals in a mating relationship with another individual of the same species (partners) will regularly express tenderness as a means to trigger reciprocal feelings, lower the partner's defence and ultimately enhance the chances of a successful relationship.  

When in "non mating mode", the standard relationship between two individuals of a given species is dominated by competition for existing resources (predation territory, food or other survival-critical resource...).  This is a situation where the relations between these two individuals can be marked by aggression and defence reflexes  ([Konrad Lorenz](http://en.wikipedia.org/wiki/Konrad_Lorenz) in his book ["On Aggression"](http://en.wikipedia.org/wiki/On_Aggression) has shown how aggression was an intra- rather than inter-species phenomenon, essentially because individuals of the same species are in the same niche).

When in "mating mode", instead, mating partners must find a way to form a permanent or temporary relationship based on mutual respect and collaboration driven by common genetic (first) and survival (second) imperatives (see the ["Selfish Gene theory"](http://en.wikipedia.org/wiki/Selfish_gene_theory) for the priorities).

In many superior primates for instance, the male will engage in gift exchanges or grooming to lower the defence barrier of the partner.  

Transposed to human social behaviour, calling your partner "Baby" suggests "I feel like protecting you" (i.e. "I'm not in an aggressive mood, please consider lower your defence reflexes").  If the partner accepts the implicit mating relationship, or consider it an option worth exploring, he or she will find a way to reciprocate the feeling through the emission of a comparable signal, i.e. welcoming the protection.

There are many other ways to express the "I feel like protecting you" message but since, in all species, babies are the very symbol of individuals needing protection (an obviously indispensable feeling if the genes are to be propagated to the next generations), it is one of the most efficient vector to convey this feeling.  Konrad Lorenz again as show (can't remember what book though) how mature individuals are universally responsive to baby features such as high pitch voices, roundish features and facial expressions (changing nappies is too recent in the evolution to effectively provoke that same "Let me do it first feeling" ;-).