Probably from the 1930’s.

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Thanks for the illustration. Did all the 37.5 calibers have the same layout? ...........

Yes, the 37.5s and the 140 series and 150 all had similar layouts (centre wheel on the train bridge, the 160 introduced the new barrel bridge with centre wheel.

............Could it be that some of these that I've seen referred to as 37.5 140 calibers are just mislabeled 19L calibers?

I'd say that's the case. All of the ones you posted look to be 19'''.
 
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D DSL
Do you think that the watch has any value, other than sentimental? Is it worth restoring it?

The dial is in really rough shape, the case is missing the bow, the crystal is broken. I think sorting this watch out would cost as much as the watch is worth.

Add to that the possibility of broken pivots, cracked jewels, damaged wheels, hairspring and mainspring and it would get very expensive, even if you could find parts.

Probably better as a sentimental memento.
 
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Thanks Jim, it's been informative. I've been going off some bad education from a couple of years ago.