Looby, the point about both sides is a bit confusing, I agree. Routinely, babies should be offered both sides in the first weeks...sometimes they will be zonked out and full and will not respond at all, and that's ok. It's not really to minimise the chance of mastistis (did I say that?) but to ensure that both breasts get the 'message' that more milk is needed.
Milk is 'ordered up' by removing it. If this happens infrequently, production lessens. After the first days, breasts work independently of each other, so both sides need frequent removal of milk. Generous producers with large storage capacities (not the same as having large breasts per se) will 'get away with' less frequent removal. Mrs Average Mum who feeds from one side only every 4-5 hours will simply not make enough milk to sustain breastfeeding or to sustain her baby.
Sometimes, mothers are (erroneously) told to only ever use one side per session. They keep the baby on that one side deliberately, and then offer the next side next time.
Some relaxed babies accept this, and take enough milk this way to tick along and survive ok, but a few weeks into it all, they get a fright - the baby is not gaining weight, and may be sleeping quite a lot (to conserve calories).
In your case, IIRC, your baby slept fine, but was clearly thriving as the weight gain was good....so very unusually, the pattern you and your baby had adopted was one that suited you both and which also kept your baby well-nourished and happy. No problem there - but for most people, this just would not work.
It's misleading to talk about feeding and sleeping cycles, as these take no account of the differences in the volume of milk different babies will take at any one time, the differences in the volume of milk available (babies never take every drop of milk - there is always some there, but there are times the breasts are less full than others), and the personality and emotional needs of the baby....stick all of those into the pot, and you will get wide individual variations.
You don't know what sort of baby you have, and what sort of breastfeeding works, in the first weeks, so it makes sense to at least offer the second side when you can. If the baby clearly doesn't want it or need it, no big deal.
Somewhere on here, I have posted links to a great study that tracked the variation in the amount of milk taken at each feed by healthy, thriving babies up to age six months - they assessed it by doing lots of test weights. The variation was from 0 (yes, zero) mls to 240 mls!
Observations of mothers and babies show that healthy, thriving babies will have a wide variation in the number of times they come to the breast, too. In pre-industrial societies where babies are carried all the time, it's dozens and dozens and dozens of times. Every time the baby twitches, it's a breastfeed. they are fine In developed countries, it's something like between 6 and 18 times, and there's a bell curve distribution ie few babies are at either end of the spectrum and most are in the middle.
Hope that helps explain it a bit more.