Weigh-feed-weigh records can provide useful information. Just be careful not to make too much out of one data point. Your baby might have a terrific feeding at the nurse's office, or he might just have a small snack. If you're really concerned about intake, you need to do several days worth of data collection. The average- or better yet, for statistical purposes, the median- intake is much more informative than any single number.
A schedule is highly unlikely to increase your baby's weight gain, unless you mean that you want to start a schedule where you offer the breast more often than the baby seems to want. A lot of moms think that stretching out the time between feedings will make the baby hungrier, so that he will eat more when he nurses. But that's not a normal eating pattern for an infant. Breastfed babies often display an eating pattern of small, frequent meals, because breastmilk digests fast and infant tummies are tiny. Most breastfed babies take about 1.5 oz of milk per hour. This can come as a surprise to a mom who sees babies the same age as her own chugging down enormous bottles of formula! All a schedule is likely to get you is a sad baby who doesn't understand why he isn't being fed when he's hungry, and potentially a lowered milk supply. Supply = demand, and the moment you restrict demand you restrict supply as well.