The case of "Health nut" and "Sports nut"
I debated whether to edit my findings in my question or ask a separate question altogether. If I included the graphs in my question, it would seem I was less interested in the etymology and usage of nut=insane than I really am.
Anyway, after some reflection I am confident in stating that today health nut and sports nut are not derogatory terms, despite Urban Dictionary's sardonic entry. Although I can imagine someone labelling a person who is careful with their diet and does regular exercise as being a health nut, I feel that health freak is more pejorative and describes a health obsession taken to extreme more accurately. Generally speaking, the current health craze, which started in the 70s, has continued to gain momentum and anyone who cares about their physical health (and appearance) is usually admired.
Television began bringing teams [American football and basketball] from across the country into the spotlight. The exposure of sports continually grew, as did their popularity. Individual sports like tennis and jogging took off (Strasser & Becklund). The health craze swept the nation [...] . By the end of the 70s sports were becoming a marketing tool and industry on a national scale.
Of course I realize that the term sports nut may mean the person enjoys watching sports from the comfort of his/her couch, but the term doesn't preclude the possibility of them actually doing sports. In conclusion the term nut is used to denote someone's passion and enthusiasm rather than allude to their mental health.
To compare usage I added the colloquial terms: sports/health nut, sports/health freak, and sports/health crazy. The first chart shows a constant rise in popularity for health nut. AmEng Ngram
But if we use the same identical terms in the British English corpus, the results are quite surprising. Health freak surpasses health nut and the terms sports crazy and sports freak are non-existent! Why? I can only surmise that the general British public is more cynical and less sports/fitness/health oriented than their cousins across the pond.
A Dictionary of Slang and Unconventional English by Eric Partridge (this 8th edition is dated 1982) confirms that "health/sport nut" has positive connotations.