Breed height standard is actually 12 inches at the shoulder, so he'd actually be a little tall f 13".
And even at 13.5 he is into breed standard weight so I wouldn't worry or consider this to be too small a size. I have two that are 11 and 12 lbs or so (rescues) and they are both in good weight for their build -- no reason to put extra weight on them.
Lots of cavaliers -- at least half of all I ever got into national rescue over 7 years -- were either under or over breed standard weights -- mostly over. So it really is just a guideline for the breed but not a requirement for the health of an individual dog whose build might not match breed standard.
On the health end of things, keeping a cavalier in good weight and even slightly on the lean side is going to mean the dog will have considerably more likelihood of living longer. A study on labradors concluded being overweight cut on average about 2 YEARS off the dog's life and that is in a breed that doesn't have endemic heart disease like the cavalier so keeping dogs fit and in proper weight is so important. Exercise is so important too and doing fun activities like agility and flyball is fantastic! Most dogs just love these activities even if done on the most casual basis.
One real weight concern are breeders who deliberately breed small cavaliers especially anything ridiculous like 'teacup cavaliers' which does have a considerable risk of introducing serious health problems in individual dogs.