"Being small, fat and asthmatic make it problematic to do much running, but he's determined to if he can."
No. The verb needs to be "makes." Why? Well, locate the subject: "small," "fat," and "asthmatic" are adjectives that modify "being." So, the subject is "being."
I myself never learned to diagram sentences (even though I taught 12th grade and 6th grade English), so I don't know if I'd say everybody should learn it (I've looked it up and find it horrendously confusing, but I've known people who boasted about their prowess doing it in school [yet whose grammar was aTROWWWWcious, so go figure]). But it might benefit some people.
I find it easier just to zoom in on the subject and go from there. Quick and effective. If you know what the principle parts of speech are, then you really don't need to bother with diagramming: after all, diagramming didn't come on the scene till 1847, yet literary greats like Shakespeare, Homer and Cicero created their masterpieces anyway.
Footnote: There are those who swear by it for improving kids' reading. Perhaps, but I was one who never even had phonics, just people at home reading to me all the time...resulting in my being able to read before I ever entered first grade. By Fall of 5th grade, CATs said that I was reading at the level of a 5th month 11th grader.
There's more than one way to skin a cat.