I don't have back problems, but I do have some surgery-related nerve damage going from the left side of my neck, across the trapezius and upper left pectoral area. Heavy basses, and basses with neck dive really start to irritate about an hour into gigging or rehearsal.
Well balanced, lighter basses really help. Here are ones I own or have owned along with approximate weight and going from least to most expensive:
Squier Bronco - A little over 6 lbs.
Squier Jag SS - about 7 lbs.
Gretsch Jr. Jet G2202 - just over 7 lbs.
Aria Pro II CSB 480 - about 8.5 lbs. This one is borderline for me.
Univox Hiflyer - 6 lbs. Slight neck dive due to body shape.
Birdsong Sadhana - 7 lbs.
Birdsong Skyrider - 8.2 lbs. Walnut = relatively heavy.
I have gigged all of these basses multiple time. My current band generally does 3 sets with short breaks over 4 hours.
The bass with the shortest reach is the Gretsch. The neck joins the body at the 13th fret. The Gretsch is about the same total length as an LP or PRS guitar. It fits in a standard PRS SE guitar gig bag. Funnily enough, I probably get the most comments on the Gretsch. Other bass players have commented on how big it sounds!
Aside from the above, pretty much any Danelectro or other hollow body is light in my experience. I agree with some of the earlier posters that poplar and basswood bodied full scale basses are generally lighter.
Here's a pic from this past summer of me with the Gretsch:
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