The idea of "strong" and "weak" progressions is more discussed in classical than jazz theory, and jazz people might superficially find it odd that "common tones" between two harmonies could be a source of weakness. The sticking point, I suppose, is that classical theory deals mostly with triads and seventh chords whereas jazz theory is built around 7-note "chordscales," and a common tone is a bigger deal when there are fewer total tones in the construction. On the other hand, the A section of Autumn Leaves, for example, is comprised mostly of progressions where only one note in the chordscale changes (i.e. where there are 6 of 7 common tones), even though the root movement is "strong."
In any case, I wrote a tune a few months ago with a turnaround of sorts that moves in reverse around the circle of fifths: D-A-E-B, all lydian chords (i.e. major7 sharp11). I wasn't sure I liked it but wanted to try it to be sure, and I think it works better than I might first have thought. Then, more recently, I listened to this Kurt Rosenwinkel tune:
Seems to my unaided ear that this is an A section built out of a few different glosses on a relatively "weak" progression that might be roughly rendered as "I-V." It works beautifully, especially the turnaround, which reminds me of mine just a little bit. So, cheers to the theory people; you know what to do with yourselves, enjoy the ride to oblivion, don't let the door hit you, etc.