I would not add weight of any kind to walking.
Those wanting to improve bone density should seek the advice of their physician. And once cleared to exercise, should seek the advice of a fitness professional.
Many resist seeking such advice and clearance. This is a bit foolish. Life is short. If you go to any fitness facility and just observe the patrons, it will become obvious that exercise increases the quality of life. And fitness professionals are there to make this as effective as possible.