Why do alkenes with more surface contact have greater London forces?
You are correct that London forces are dependent on the size of a molecule, but think about why this is. One reason is that a larger molecule tends to have a greater surface area than a smaller molecule, and thus there is more surface area available to interact via London (and other) forces.  

Also as stated in this Wikipedia article:  


  London forces become stronger as the atom in question becomes larger, and to a smaller degree for large molecules. This is due to the increased polarizability of molecules with larger, more dispersed electron clouds.