In my big prison where inmates wouldn't use weights in the yard or the common room I just tried removing the yard designation and several people immediately started using weights in both the common room and the canteen. It seems that no-one will use weights in the yard, common room or canteen during free-time or work time if there's a yard available for jogging (prisoners will still use other types of objects in all three areas) and they never use weights in the yard during yard time either. I have the gangs option disabled so that's not a factor.
In that prison there's no point putting weights in my yard because if the area is designated they'll always jog there instead and if I remove the room designation they stop using all resources there. This is a shame since common sense (and the objects menu room filter) says that yards are the obvious place to put your weights benches. (Unused weights won't help snapshot hunters either...)
It's still worth me having some weights in the canteen (when I have a yard) since prisoners will use them while confined there during eat time and it's definitely beneficial to put weights in cells for any inmates on permanent lockdown (if they have exercise needs - not everyone does).
My issue is not universal or consistent though. I have two entirely separate games on the small Paradise City map and on one save the prisoners use the yard weights and never jog while on the other it's the opposite. I don't know what factor is governing this - I wondered if it might be related to suppression but I tried adding three dozen armed guards in the yard and neighbouring canteen in my big prison and they couldn't convince the fanatical joggers to try the weights instead.