Ridge beat me to it, suggesting you get two day-old chicks, not just one, and not just because it needs a friend.
When adding new chickens of any age, a single one gets all the focus and attention, while with two, the attention is diffused over the two of them. In addition, Buffs are very docile breed and a single would have a difficult time gaining self confidence. With two, they will give each other the confidence they need to cope.
The two and three week age difference isn't insurmountable. But you do need to partition off the new ones until they grow a bit. Have the brooder in proximity to the older ones so everyone knows they're part of the same flock. If you haven't already put the two older groups together, start doing it immediately. The sooner they all become a flock, the better.
After they've all been in proximity for a week, try putting them all together. Referee, but give them a chance to establish a pecking order. Step in if you see a single chick getting mobbed by several bigger ones at once. In a few minutes, they should have things worked out. If not, use your position as "flock leader" to discipline any trouble makers by poking them on the back each time they cause trouble. This is how chickens do things when younger ones step out of line.
The ages are still so close, you should have no trouble pulling this off.