Jelly, 6 bytes

S÷@×"S

or

÷S$×"S

Input is via two command-line arguments, masses first, coordinates second.

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Jelly, 6 bytes

S÷@×"S

or

÷S$×"S

Input is via two command-line arguments, masses first, coordinates second.

Try it online!

Explanation

S       Sum the masses.
   x"   Multiply each vector by the corresponding mass.
 ÷@     Divide the results by the sum of masses.
     S  Sum the vectors.

or

÷S$     Divide the masses by their sum.
   ×"   Multiply each vector by the corresponding normalised mass.
     S  Sum the vectors.

Jelly, 6 bytes

S÷@×"S

Input is via two command-line arguments, masses first, coordinates second.

Try it online!

Jelly, 6 bytes

S÷@×"S

or

÷S$×"S

Input is via two command-line arguments, masses first, coordinates second.

Try it online!