Robert, add sugar a little at a time (as simple syrup) and taste test
the result to arrive at the best balance. The sugar will balance
against acid and alcohol. Getting that fine balance between the three
is where the "art" of winemaking enters the picture, assuming your
winemaking techniques are sound.

It is best to sweeten a sample of the wine first, recording exactly
how much syrup you add to get the right taste. Then you sweeten the
remainder using the same proportions. For example, if you have a U.S.
gallon of wine and use a 250 mL sample and add x amount of syrup to
achieve the taste you want, you then add 14x to the remainder to
approach the same result. For an Imperial gallon using a 250 mL
sample, you would add 17x to the remainder.

By all means, stabilize before sweetening.

Jack Keller, The Winemaking Home Page
http://winemaking.jackkeller.net/