My understanding is that height/weight requirements aren't DODMERB issues. Rather, the SA must determine whether to admit a candidate who doesn't meet the requirements.
They will tape you. DS has always been underweight, and has been taped since he was 17. It isn't a big deal. The only thing is if you than fall below the allowed tape measurements.
They do taping not only for underweight, but also if you over the weight limit before any corrective action is created.
If the minimum is SA specific, are they at least similar? Is there a chart for minimum weight for USCGA? I found the maximum weight/height charts but no minimum. DS is on the small side. He is attending AIM session 2 so I suppose he'd find out then if it is an issue but I would like to be prepared before he goes.
There is a minimum for all branches, but the academy can waive it to allow you in. They did for me. However, once in you should work on boosting your weight to the minimum, or you will pay for it later (like me...).