Linear density would be mass per unit length so units will be kg/m. Using a heavier string (assuming the dimensions of the string remain the same) will cause it to increase because you increases the numerator (kg) without changing the denominator (m). Using a thicker string should increase it because again, you will have more string per unit length. Assuming the dimensions of the string remain the same, using a denser string should also increase it for the same reasons as above.