If I resample the training dataset to 10:1, I don’t think I should put any weights. Is that correct or we still need to put some weights to the smaller class.

I think this has essentially (approximately) the same effect as weighting. Say you have made a prediction on a certain minority sample. If you then make the prediction again (due to the replication via  oversampling) you apply the gradients twice, essentially. This is somewhat analogous to increasing the weight of the loss by a factor of 2 for this data point.