Earlier quoted context omitted.
First, just to clarify - there are different ways to count the quantum fields, just as there are different ways to count particles, as the article points out. You really need to specify the premises you're using to count them. But either 17 or 37 are natural counts. 17 is a somewhat simplified version, which ignores quark color charges and groups the W and Z bosons together. Here's how the list of 37 typically breaks…
I'm a bit surprised that the weightier generations of fermions are categorized as fundamentally different fields. Is this a crutch/temporary classification that we expect to be resolved with further research, or are there real indications that the apparent similarities between e.g. up/charm/top are fully independent manifestations?
"No idea, bro!"
It's one of the biggest open questions about the Standard Model, and it's considered an indication that the model is probably incomplete.
Btw you mentioned "weightier generations", but mass is a consequence of the difference between the generations, not the fundamental difference. Before electroweak symmetry breaking, those particles had no mass, but they already existed as three distinct generations, with different Yukawa couplings. When the Higgs field acquired a vacuum expectation value, those different couplings became different masses.
The Standard Model treats the number of generations and the Yukawa couplings as fundamental inputs to the theory. There's a Nobel Prize waiting for whoever figures out whatever might be behind this.
Even string theory doesn't solve this. Calabi-Yau manifolds provide a model which could explain it in theory, but no actual, concrete solution has been found.