Not only that, but you might consider that power armour actually aids and adds to strength, probably at a penalty to agility.
Why the penalty to Agility?
Here's the description of Power Armour from the Wh40K rulebook (3rd edition):
This is a completely enclosing suit of armour as worn by Space Marines. It is made from thick ceramite plates and would be heavy and cumbersome but for electrically motivated fibre bundles implanted in the armour that replicates the movements of the wearer and supplements his strength.
Meaning that a set of Power Armour isn't really a rigid full enclosing suit powered by servos and pistons, but rather a multi part exo-skeleton with artificial muscles on the inside of the suit ("electrically motivated fibre bundles" = muscles basically). Artificial muscles designed to mimic human muscles would be a lot more dextrous than a suit made up of a complicated system of servos and pistons, meaning that the armour itself should therefore only limit the movements of the wearer in a negligible manner at the very worst.
So while I (as a GM) might ask a player to at least remove his or her gauntlet from the power armour if he or she wishes to do some fine manipulation with his fingers (like tinkering with small wires in a security lock or doing sleight of hand tricks) or otherwise suffer a penalty, other Agility checks (besides Silent Move which was adressed in the errata) woulnd't have any penalties at all.
As for the weight of it, it would definetly be no point in wearing a suit of power armour if it wasn't able to keep itself upright. The +10 or +20 bonus for power armour is clearly intended to be the additional strength you get in excess of wearing the suit of armour (provided that it still has power that is).