"Mach's Principle" is the rather vague philosophical-physical notion that inertia — how hard it is to push a mass around — is related to other masses in the universe. It's named for philosopher-physicist Ernst Mach, though others came up with versions of it earlier. A classical example: take a bucket of water, set it on a turntable, and spin it. The water sloshes outward. But if there were no other objects in the universe, how could the bucket "know" it was spinning? Would the surface of the water then stay flat? (Easier asked than answered!)
Mach's principle appealed greatly to Albert Einstein, though people argue how significant (or real) the principle is. Never mind; take Mach seriously for a moment. The big trick of Einstein's theory of gravity is that it turns gravity into geometry. "Space tells matter how to move; matter tells space how to curve," in John Archibald Wheeler's mantra. Distances are affected by mass. A ray of light's path bends when it goes near the Sun. The light is still trying to move in a straight line but "straight" is different in curved space.
Which brings me to my tiny-silly idea, hatched during a walk to the subway a few days ago. Science-fiction readers of a certain age (e.g., mine) will remember E. E. "Doc" Smith's Lensman stories written in the 1930s and '40s. A central feature of those tales was the "Inertialess Drive", a technological plot-device that let the characters travel across and among galaxies quickly enough to fight aliens and save the universe.
So put the three together: Mach + Einstein + Smith. One can clearly work out mass distributions that stretch space locally. Would such a configuration of bodies — you'd probably need to use black holes — cause local inertial properties to change? Could "stuff" inside the magic zone "weigh less" because it's now effectively farther from all the other matter in the cosmos? It's not even a half-baked notion but maybe, with a lot of hard work and calculation, somebody more expert in General Relativity than I could compute examples to show the effect, if it exists. Maybe somebody already has.