Training with weighted labels

Hi, I am now doing a multi-label text classification now.

For my dataset, some label is more important than others. more precisely, the order of the labels. The first label is the most important.

The first thought of me is just brutally change all the targets of labels of the first order label to 1, others lower, like 0.8, trained BERT with linear layer, BCEWithLogitsLoss.

An example:
Suggest that there are only [A, B, C] labels in the dataset.
I have 2 training data: the first data label is [A, B], the second one is [C, B, A].
If I adjust the target to:
data1: [1.0, 0.8, 0.0]
data2: [0.8, 0.8, 1.0]
(the index matches the label set [A, B, C])

Will there be any problem when training or is there a better way to achieve the weighted labels?