If your 1 year old is peeing out of his diapers then you might need to move up the next size bigger which would give your baby more absorbency in the diaper.
Also if you haven't done so try pointing his penis downwards in the diaper and make sure you pull out the standing leg gathers around his legs.
Another thing to check is the tightness of the babies diaper. Make sure the diaper is not too loose.
Make the diaper tight enough so that it won't leak out the waistband so easily. You can tell how tight a diaper is by placing your two fingers between the waistband.
If the two fingers can go under the diaper waistband then it's usually snug enough without the diaper being too tight.
If he still leaks out his diaper and you're using disposable diapers then you might try cloth diapers for overnight since cloth diapers tend to not leak when a baby is in the lying down position.
You could also even try placing some plastic pants over the babies disposable diaper during the night which will help contain the leaks until you can change his diaper in the morning.
You might also have to get up in the middle of the night and change his diaper so he will have more room in the next diaper to hold his pee in and then won't overfill the diaper.