A polypeptide in its native conformation has weak interactions between its R groups. However, when that same polypeptide is denatured, these R groups similarly interact with water. Why, then, is the native structure more stable than the denatured one

A protein is more stable in its native form, because apart of weak interactions between R groups, it also presents other stronger interactions, as those including covalent bonds

Explanation:

For example, covalent bonds between sulfur atoms when disulfide bridges are built. These links are very difficult to break and maintains the protein shape. Disulfide bonds are a few but they use to incide in the structure of native proteins