In general, about 4 ounces less than what it weighed before drilling; possibly as much as 6 or 7 ounces if the ball driller added what's known (somewhat oxymoronically, if you think about it) as a weight hole, which changes the ball's internal balance and thus the amount by which it hooks.
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So far I have found it can cost from $30 to $50 for drilling a ball. It's an additional cost for finger inserts - between $10 and $20.
The end weight of the ball must be no greater than 16 pounds, with a 3 ounce variation for top weight, 1 ounce for thumb weight and 1 ounce for side weight.