One website that discusses vests and shoes, including information on a research study, is from Margaret Martin: https://melioguide.com/balance-exercises-for-seniors/minimalist-walking-shoes/ .

On weighted vests generally: americanbonehealth.org has a short discussion of the pros and cons along with study references: https://americanbonehealth.org/exercise/weighted-vests-for-bone-health/ . Of course, you have your own trusted medical advisors as well.

Oregon State University Extension has a program using weighted vests: https://extension.oregonstate.edu/bbb , named Better Bones & Balance. They have in-person classes in the area around Corvallis and Albany, Oregon (and a few other sites), and have a DVD. They also have an instructor training program (summer, partially online).

I have a weighted vest (Margaret's recommended) and plan to start using it soon on the treadmill and/or via the BBB program (I purchased their DVD, but haven't viewed it yet).

My approach as I navigate trying to improve bone health without injury (yours might vary):
1. I read the information and at least the Introduction and Discussion/Conclusions of the studies. I also will look for "other research" that cites these studies, to see what new information is available.

2. After I feel like I understand enough to at least personally justify my actions to myself, I will then begin exercises slowly, doing any strength or step exercises without the weighted vest until I am happy with my form (if ever). I have learned for me an injury is a greater set back then the chance of swifter improvement. And I do appreciate the time imperative, as I am in my mid-60s and fighting on the edge between osteopenia and osteopororsis, with bone loss due to taking aromatase inhibitors.

Best of luck!