What does sample_weight mean in LinearSVC in scikit-learn?

Question

Mathematically, what does sample_weight mean in sklearn.svm.LinearSVC as well as svm.SVC? According to what they say in the document, I assume that the scales directly change C for each sample, that is, for the i-th sample, the penalty is Cw_i.

Well, but I executed the code here SVM: weighted samples Using SVC and LinearSVC (just change the class to LinearSVC) and it seems that LinearSVC gets the sample results regardless of weight. The developers say that Linear SVC is "less sensitive to sample_weight", but in what sense is it less sensitive (mathematically)?

Another thing - is there a way to use SVC without interception? This is why I use LinearSVC ...