So how does this whole weigh-in / tape out situation work?
If you weigh-in and you're below the screen weight, no harm, no foul. Go on about your business. By the way, there are minimum weights and believe it or not, there was a guy in the Aggie Band two years behind me who had to gain weight. I think he was like 6'0" and 135 lbs or something anorexic like that.
If you're over the screen weight, now we have to take a look at the allowable % of body fat for the given age group. This is detailed in Table B-2 on Page 21 of AR 600-9. So, let's say we're talking 21-27 years old, the allowable body fat % is 22%. Now this is where it gets interesting. How the Army calculates body fat%. It all comes down to the delta between the circumference of your waist and the circumference of your neck.
So let's say I have a 36 inch waist and a 17 inch neck, the Army method takes 36, subtracts 17 and yields a "circumference value" of 19.
Now on page 28 of AR 600-9, you take that value and match the column associated with my height (74 inches) and you find the %body fat to be: 16%. That puts me under the allowable value of 22% so I'm in compliance with the height weight standard.
Let's say that I gained a bunch of weight around my midsection and my waist was 39 inches and my neck has slimmed down to 15 1/2 inches. My "circumference value" is now 23.5. Plugging that into the table using 74 inches for the height again, my body fat % shows to be 24% so I'm now out of compliance with the 22% standard.
Once you're out of compliance, you get on a weight control program where you now have to weigh-in more frequently and you have to participate in remedial physical training. Just like therapy, this can be group or individual.
I was pretty fortunate that as a cadet, we had a military advisor who had been in the Aggie Band about 14 years ahead of me. He took a special interest in me and in addition to the required remedial PT, he made me come running with him twice a week. This was a good 3-mile run from The Quad out across the tracks to Research Park and back. Did I mention that I hate running?
With the extra attention, my weight hovered around 202-206 lbs. In preparation for going to ROTC Advanced Camp, I put a little extra effort into it and when I weighed in, I was on 202 lbs. Being under the 206 screen weight meant no tape test so I was plenty happy with that.
After 6 weeks in the field at Fort Lewis, Washington, eating Army chow and working 18 hour days (or whatever), I lost an amazing amount of weight and got down to 192 lbs. That is the lowest I've been in my adult life. At 192, I was anorexic looking. I even put on a pair of jeans that I hadn't worn since 10th Grade.
So, back in the real world, I gained back up to 205-210 lbs or so. A constant struggle to try to get down to 206 prior to commissioning. I made it. It's funny after listening to the Army tell me repeatedly how fat I was, I get a kick out of looking at the pictures of when I graduated from A&M and how relatively skinny I look.
5 months on Active Duty at Fort Knox, similar story. I weighed in at 205-206 every weigh-in. That usually involved a few days worth of starving myself and of course we were doing plenty of PT in the old WWII Barracks area where they filmed "STRIPES".
My next 6 years in the TXARNG were a struggle. The good news was that in the National Guard, we only did our Record APFT and Weigh-In once a year. So, I could cram a little before hand. But by this time, I was up in the tape-test all the time situation.
I gained weight during both of my wife's pregnancies and I still hated running

So, I did tape out a few times at 215-219 lbs but, it was a lot of stress to have this situation looming over my head.
Eventually, I didn't tape out and had to go on remedial PT, weight management counseling, etc. What really frustrated me the most was the fact that when things like performance reviews come up, height-weight and APFT performance is a factor. The point I want to make here for your son to consider is that his ability to make weight and his speed in the 2-mile run will be factors in how his leadership is evaluated in the military. These metrics don't mean anything in the civilian world so I've done well in the real world. But it was frustrating having my accomplishments in the field diminished by my height-weight/APFT scores.
I'm sure I've just opened myself up for plenty of ridicule/criticism but... bring it on. I'm a former Army Officer

I can take it.
I hope that your son chooses to attend Texas A&M on an Army ROTC Scholarship. That is an experience and opportunity that will serve him well in life.