Dwarves were in fact naturally resistant to the corrupting effects of Sauron, perhaps moreso than even Hobbits.
Of the Rings of Power and the Third Age:
Sauron gathered into his hands all the remaining Rings of Power; and he dealt them out to the other peoples of Middle-earth, hoping thus to bring under his sway all those that desired secret power beyond the measure of their kind. Seven Rings he gave to the Dwarves; but to Men he gave nine, for Men proved in this matter as in others the readiest to his will. And all those rings that he governed he perverted, the more easily since he had a part in their making, and they were accursed, and they betrayed in the end all those that used them. The Dwarves indeed proved tough and hard to tame; they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows. They used their rings only for the getting of wealth; but wrath and an over-mastering greed of gold were kindled in their hearts, of which evil enough after came to the profit of Sauron.
LOTR Appendix A:
For the Dwarves had proved untameable by this means. The only power over them that the Rings wielded was to inflame their hearts with a greed of gold and precious things, so that if they lacked them all other good things seemed profitless, and they were filled with wrath and desire for vengeance on all who deprived them. But they were made from their beginning of a kind to resist most steadfastly any domination. Though they could be slain or broken, they could not be reduced to shadows enslaved to another will; and for the same reason their lives were not affected by any Ring, to live either longer or shorter because of it.
Turned into shadows being 'turning invisible', the wraithform that leads eventually to ringwraiths. The Ring, as an extension of Sauron's power, this suggests, could incite Gimli to anger and rash action and to greed, but could not directly influence his mind to defend itself. Bilbo's band of dwarves seemed similarly unaffected by the Ring in their presence.