How does natural selection favour large body mass and size (or so it seems)
Well first of all I don't know if natural selection favors larger animals - most of the living things in the world are single celled.  

Still there are advantages to being larger.  I don't know if I can list them all!  In no particular order: 

1) Living things that are large are more metabolically efficient. The amount of food required goes as a 3/4 power of the size of the animal.  Thus a cat 100 times the mass of a mouse requires only 31 times more food.  I don't believe that it is not known how this works. 

2) r vs K selection: larger animals have greater individual "value".  Smaller animals tend to live by r-selection - they are cheap and reproduce in large amounts, then lead short and highly competitive lives where most offspring die without reproducing.  Larger animal tend to live longer and reproduce offspring with a greater chance of life. In the extreme case you can compare a cockaroach to an elephant here.  This is not a hard and fas rule, but cheap offspring do tend to be small.

I seem to remember that there are lots of other surveys done and body size correlates to life span and any number of other attributes, which I will try to add after I get some sleep unless someone slips in and lists them all. 

3) Cope's rule - an observation as much as a rule that size must convey some advantge because most animals become larger the longer they are around.  Not always true, but there is a trend that the longer evolution works, the more likely a large animal will show up.  This might be because as niches for smaller animals are filled, niches for larger animals become more accessible?