I wear a weighted vest for a 2 mile walk each morning. I don't think there is any study showing weighted vests increase bone density. If anyone has seen one please let us know.
I'm going to walk each morning because I want to and it's a way I support my wife being active, so why not wear a vest that provides more impact and resistance than just walking. Seems like it should support bone density and bone strength. But I don't rely on the vest for improving bone density. Twice weekly I do free weights roughly per the LIFTMOR trials for exercise proven to increase bone density. And I do body weight exercises for core and theraputic issues twice weekly. And I do balance exercises for fun.

I wear a vest my wife bought so it's a woman's vest but it works well. It is pricey but it has some nice features like the weights are what they call soft flex which means they do not feel like metal and they are 1" by 3" by 3/8" of a soft pliable material. Why does that matter? Well if you fell with a vest or back pack of hard weights with hard edges that could be bad. This is the only vest I've tried so I don't know what the other brands are doing.
The maker of these vests is https://ironwearfitness.com/. I have the CoolVest Short women's model.

I weigh 150 lb and started with 9lbs and now I wear 18lbs and I hardly notice the weight except when putting it on and taking it off. Some follow the backpacking logic of a hip belt to reduce strain and weight on the upper back but I want the weight/force going down the full length of my spine. I personally do not do various exercises with the vest. Vests do not appeal to me as a way to do resistance exercise. Each to his own.