Weapons and shields are permanents, so weapons and shields should count.
Why wouldn't they?
To be honest, This thing's dealing between 6-9 damage on average, so its cost is fine.
Otherwise, sure.
You also have to consider the extreme cases that can occur for decks built around the card in question when considering cost balance.
If used with the average deck, it will only pop 6-9 damage because most players only have 1 stack of pillars / pendulums plus a sword and shield.
If you were to build a deck around this card (like people would very likely try to do), you can easily get over 5 different pendulums and pillars in play after the first two to 3 turns. Also add in the sword and shield as well. That gives you 7 permanents for a total of 21 damage!
So at the very least, it should have the same cost as unstable gas unless there is some kind of counter balance.
Having only the owner's permanents count toward damage helps, but only a little. At most it carves back about 6 to 9 points of damage. Decks geared toward spamming a full field of pendulums then using this will still get to output tremendous damage. So I think its still a little OP at its current state.