Non-uniform class occurances in input data for classification task - how to tackle it?

So, I gathered political articles for my thesis, now I want to be able to classify given text. Though the classes distribution is actually crazy.

• Class 1: 964 docs
• Class 2: 37,020
• Class 3: 640
• Class 4: 2,675
• Class 5: 793
• Class 6: 23,160
• Class 7: 2,665

Such a skewed data is obviously going to favor classes 2 and 6, though I thought about elevating the difference from last layer for classes with lower observations, is that worth a shot? Or it will actually create overfit for these classes? Unfortunately I can’t scrap more data, the websites with articles doesn’t have any more (at least now). Of course any data augmentation is not possible.