I would try to use a weighted vest or a weighted backpack while walking instead of ankle and hand weights. But, I agree with most of the answers others have already provided here. Also, if you or your clients live close to the ocean, a nice walk on the beach with the water level between the ankles and the knee would also do the trick.
Unfortunately ankle and hand weights do not provide the best method to build bones.
a) Jonathan and Shay point out the drawback of weights that are too light;
the load is not enough to improve bone strength
b) Stephen and Michelle point out how the extra weight throws off a person’s
gait and can cause injuries.
The weighed vest idea may work (if the person has no back industries); the stress caused by heavy weight further from the center of the boy (i.e. on the ankle or in the hand).
(Resistance training would improve bone strength. However your client seems to be bent on walking; I’m not so sure how the client will respond to using weights.)
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.