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We've been over this.
The Ring of Power corrupts those around it by promising to fulfill their darkest desires. It channels their urges to get what it wants.
It wanted Gollum to hide away under a mountain until its master could return with his armies.
Hobbits and River Folk don't seek power. They want to be left along, smoke their pipes, and have lots of fat, happy children. As such, they have a natural defense to the ring's influence, but they are not immune to it. It makes them covetous and protective of the precious, even if they don't seek to use it for their own benefit.
We see the Ring of Power turns Gollum and Bilbo and Frodo invisible, but is that what it would have done for Boromir? For Gandalf? For Gimli or Galadriel? Almost certainly not. We saw in a flashback what it could do on Sauron's finger, and the only thing it did for Isildur is quicken his death. Gollum was seduced and wanted to hide away. Bilbo was a burglar wanting to sneak past a dragon. Frodo wanted to sneak into Mount Doom.
So what does Sam want? The only thing Sam wants more than to return to the Shire is to ensure his best friend makes it home with him. Sam cannot carry the Ring, not because he is weak to its influence, but because his best friend wants it. Frodo has been corrupted, and would fight Sam if he tried to take it. They tried taking turns, but Sam learned what it felt like to want the Ring, and knew he couldn't do it again.
But he could carry his friend, burdens and all. The ring could not drive a wedge between them, because Sam didn't seek to separate Frodo from the Ring. Sam's singular focus was getting to the end of their shared quest so that they could get home together.
If you put the Ring on a mouse, then whoever is carrying the mouse would be tempted to take it away, and the mouse would use the power of the Ring to keep it. Sam was resisting the temptation of the Ring, and the Ring was fighting back as hard as it could. It fully corrupted Frodo in the end, and it was only Gollum, who coveted the Ring more, who was able to take it away.
Fate, luck, the will of Eru, call it whatever you want, but Hobbits have the superpower of quiet contentment, and that's the only thing that can beat a lust for domination of the Valar, the Maiar, of Elves and Men and Dwarves. It's why Gollum hid away without conquering the goblins living above him. It's why Bilbo could roll with dwarves and give up the Arkenstone. It's why Frodo could walk into Mordor, right to the edge, knowing the journey was going to kill him. And it's why Sam could carry Frodo the rest of the way.
