big baby!

so my son is turning 4 months old on the 1st of July. He was born weighing 9lbs and 4 oz and 22 in long. Well the other day I took him to the doctor to check out a cough he was having and the nurse was shocked when she saw he weighed 20 lbs already! not only that he's 25 in long! I'm just really worried that he's going to outgrow diapers too fast since he's already in a size 3 and approaching size 4 fast.

For reference, my husband is 6 ft 2 in and is the shortest of the men in his family and my father and all the men in his family are over 6 feet, some a little over 7 feet.

does anyone have any suggestions on what to do if he outgrows regular diapers??? just stressing that he won't make it to a year and I don't know any alternatives :/