I saw only now the revamp on "your pets" page, and I found a new "value", Tier... My active pet is "Tier: 4", while all the others are "Tier: 1"... But, what is "Tier"? :D

Pet Tiers are based on their battle stats, the higher the stats the higher their tier. Weapons are also listed in tiers and if your Pet is in tier 4 for example it can use weapons from tier 1-4 but none that are above that. All this is part of the current revamp of the battle system. You can read more about it on the Battle forums, for example in this thread here:

I&;m looking to trade for a Black Jaguar Egg Doll

Thank you really so much! ❤

You are welcome, glad I was able to help! :)