The hydra is classically described as growing two heads back for every one cut down. Mjolnir, theoretically, became exponentially heavier to the unworthy.
What other Gods, creatures or equipment have powers that are tied to doubling or exponential characteristics?
Not associated with any "gods" as such; there are a large number of folktales containing items with exponential growth.
The Aarne-Thompson classification system groups many of these stories into category, AT 565. One of the best-known of these is Why the Sea is Salt, where an out-of-control salt mill grinds out an endless amount of salt.
The goings-on in The Sorceror's Apprentice certainly smack of the Lernaean Hydra, but that one is more literary than folkloric.
And of course there is the matter of how darn fast that beanstalk grew...
There is an Asura in Indian mythology called RakthaVija. It is difficult to see if his growth is technically exponential. But as the myth goes, he is able to replicate another version of himself from every drop of blood that touches ground ; quite handy skill in a battle.
As the story goes on, the primary godess (Durga, if I remember correctly) who was meant to kill this asura had to seek help of another godess (Kaali) whose one of the primary instincts is to drink blood. She helped the battle by drinking each drop before it touched the ground. Talk about specialized skill set.
I only know of a few that are seen as magical. However I'll do some research and come back to edit this answer when I find some more, but for now I'll list the ones I know.
The Armour of Achilles: Made by Hephaestus and said to be completely impenetrable.
The Helm of Darkness: Made by the Cyclops for the Lord of the Underworld Hades. It turns the wearer invisible and is said to bring out your darkest and deepest fears.
Apollo's Bow: It can cause health or famine and in some stories, death.
The Hide of the Nemean Lion: A hide worn by Hercules, or Heracles, and was able to endure every weapon and was unbreakable.
