For the first few weeks, baby's milk intake increases - however, milk production at this point is still at least partially hormonally regulated and supply is still evening out.
Between about 1 and 6 months of age, a breastfed baby's milk intake has been found to remain about the same (with the exception of "growth spurts" when it temporarily increases before going back to normal). So no, there is no need for mum's body to produce more milk as baby grows :). However, if demand should increase for any reason then yes, she would start to produce more in response to the extra milk removal.