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Although I do not believe I ever met him, Jerry Crownover, a former professor at my university, in his column in a local agricultural newspaper, wrote about a phrase his wife questioned. His wife wanted to know its origin.
I found and sent to him the following from the online Oxford English Dictionary:
b. esp. Physical condition, as in good case (arch.); also simply, in case, out of case (? obs.). Also, esp. in U.S., spec. of tobacco.
1640 in Arch. Maryland (1883) I. 98 Bad Tobacco shall be judged..[what is] sooty, wett, or in too high Case.
1640 in J. Nicholson Minute Bk. War Comm. Covenanters Kirkcudbright 6 Oct. (1855) 60 Ordaines..that William keip the horss in good caice.
1655 T. Stanley Hist. Philos. I. iii. 111 By this means their horses are the better in case, but the worse for service.
1674 W. Cunningham Diary (1887) 3 The houses are out of case.
1693 W. Robertson Phraseologia Generalis (new ed.) 315 In good case for flesh, pinguis.
1704 Swift Full Acct. Battel between Bks. in Tale of Tub 240 Their Horses large, but extreamly out of Case.
1725 R. Bradley Chomel’s Dict. Å’con., Jockey..one that brings Horses into Case.
1755 Johnson Dict. Eng. Lang. (at cited word), In ludicrous language, In case is lusty or fat.
1800 W. Tatham Hist. & Pract. Ess. Tobacco 37 It must be stretched gently over the ends of the fingers and knuckles, and if it is in good case, i.e. plight, or condition, it will discover an elastic capacity.
1808 Scott Marmion i. xxi, Our Norham vicar..Is all too well in case to ride.
1845 G. Dodd Textile Manuf. 132 An exposure to the air for..about five weeks makes the leaves of tobacco elastic and tough, and slightly covered with a glossy kind of moisture. The tobacco is then said to be in case.
1852 H. B. Stowe Uncle Tom’s Cabin xii. 72 What he would sell for, if he was kept fat and in good case.
1865 Trans. Illinois Agric. Soc. 1863 V. 667 The fires should be suffered to go out, and the tobacco be suffered to come in case, or get soft again.
1944 Dial. Notes Nov. 65 In case: adj. phr., in proper condition—cured and having the correct amount of moisture to ensure handling without injury or loss.
If anyone has more insight, I will forward Jerry the link to this thread.