I know a few men, most of them overweight, whose penes (notice the Latin plural) completely recede inside their bodies when soft; only when aroused at least somewhat does the glans protrude at all and then only an inch or so. I've never seen any of them erect so I don't know how much longer they get. What's going on here?

That would be called a micro penis I believe.

It is not that it is "inside" the body" but merely that roles of fat would be hiding it. If it is not something from birth

The micor penis is a medical condition that happens in about 1/2 of one percent of males

Here is a link
Micropenis - Wikipedia, the free encyclopedia

The Latin plural of penis is penis. Penes is a preposition that means "in the power of, belonging to."

Males have only one.

The anatomy of a D!ck (Notice, colloquial english).

The penis (formal english) is attached at the hip bellow and before the anus (proper name for an assh0le). The actual length for the penis is over a foot long but most of that is internal. The penis is attached there so it has a solid thrusting base and doesn't flop around. Most animals have a pubic bone that slids up the shaft instead of the erectile tissue humans have.

So as a man gains weight the fat cells around the penis, the pubic mound, grow as well. This will hide a lot of the length both flaccid and rigid.

There is also the grower vs the shower debate. Some men's penis will grow while others will just gain girth. Could be that the person in question just has a small penis (That is english for a tragedy?)

Why are you so curious? (That is a common English question.)