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 one describes tenderness as a way of consolidating mating bonding. It is indeed a well documented pattern in many superior animal species that individuals in a mating relationship with another individual of the same species (partner) will regularly express tenderness as an unconscious way to trigger a reciprocal feeling, lower the partner's defence and ultimately enhancing 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 aggressiveness and defence reflexes (Konrad Lorenz in his book "Aggression" as shown how aggressiveness was an intra rather than interspecies phenomenon).
When in mating mode, instead, the individuals 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").
In many superior primates for instance, the male will engage in gift exchanges 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 babies are the very symbol of individuals needing protection (an obviously indispensable feeling if the species is to pass generations), it is one of the most efficient vector for 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" ;-).