Copper is Venus in the alchemical scheme, marked with a circle set above a cross. The same sign is used in biology and astronomy for the female and for the planet, and its survival in that role is one of the more visible remnants of alchemical notation in ordinary modern use.
The reasons given for the association are worth separating from the association itself. The link is attested from late antiquity and stable by the medieval period, in the same body of texts that fix the other six. The explanations offered are later, or reconstructed: that polished copper and bronze made the mirrors of the ancient world, and the mirror is Venus's attribute; that Cyprus, the island the metal is named for, held a major cult of Aphrodite; that copper's characteristic corrosion products are the green of vegetation and growth. All three are plausible, none is documented as the original reason, and the honest position is that the correspondence is well attested while its origin is not.
The Cyprus connection at least is solid on the linguistic side. The Latin cuprum is a contraction of aes cyprium, the metal of Cyprus, which supplied a great deal of the Roman world's copper.
Copper's compounds carry their colour strongly. Verdigris, a copper acetate, and the mineral malachite, a copper carbonate, gave painters and dyers a range of greens; azurite gives blue. Egyptian blue, the first synthetic pigment, made from about the third millennium BCE, is a calcium copper silicate. The green patina on old bronze and on copper roofs is a mixture of carbonates and sulfates, and it is protective, which is why it is left in place.