Years ago I lost 50 lbs in 6 months, mostly by hiking on hills in a 40lb vest.
I was perfectly fine with hiking with all that weight, I never had problems until I started trying to run on the beach with the vest on.
Interestingly, everyone told me that I would have knee problems, but my knees never bothered me at all. What started giving me problems was my heels (my achilles tendon, I assume).
So, I'd definitely recommend walking/going uphill with the vest on, but not running. At least, not with the vest fully loaded.