Liz, the empty breast thing is very misleading....to check there is milk and assume that the baby does not want any more from side two if there is some still in side 1 might seem logical, but it actually isn't!
You can never totally empty the breast, though clearly the breast can be fuller/emptier at different times.
Babies often drift off while feeding on side one, then if they go onto side 2, they start to feed vigorously again, even if there is milk in side 1 (and of course there always is). The faster flow of the second side stimulates them to feed more, and also removing the milk from side 2 encourages more milk to be made....and the opposite is also true, that is, not removing the milk from side 2 encourages less milk to be made.
Now, for many women, this doesn't matter. They have more than enough milk for their baby without each breast being used at all/most feeds. Everything is just fine and dandy....and in a few cases, mothers who routinely feed on both breasts can become overwhelmed with too much milk, and then they have to make a conscious decision not to offer both.
If there is a concern about a baby's weight, then it would be really important to ensure both breasts are offered every time.