You provide just the weight for the positive class. The formula is in the docs 556.:

l_n = -w_n * [p_n * log(sigmoid(x_n) + (1-t_n) * log(1 - sigmoid(x_n))]

However, this parameter can influence the recall (true positive rate / sensitivity) vs. precision (positive predictive value). You can read more about it in this Wikipedia article 242.
In case you have binary labels the negative classes will be influenced jointly. I’m not sure what would happen if you use soft labels.