The one aspect of this quote which I can point to in Chazzal is the fact that Hashem will punish the child for his fathers sins when the child continues in his fathers ways. This is found in Brachos 7a and Sanhedrin 27b.
The explenation given כי עוון של דורות חמור יותר מעוון של פרט אחד does not appear there. In fact by reading the gemara in Sanhedrin and the psukim (especially Shmos 34 7) in context, the point is Hashem in his merciful kindness does not punish immediately but rather waits for repentance, up to the third and forth generation. If that does not happen, he will punish that generation, however all past misdeeds of the last generations which were hanging up in the air will come crashing down at long last.
[Another point from the gemara there is that we are obviously discussing a situation where there was no possibility to reprimand the sinners. Anyone at any time can be punished for someone else's sins if they had the opportunity to reprimand them and did not.]
See also Sanhedrin 39a where this pasuk is the basis for one of the only three extent parables out of three hundred fox parables which Rav Meir had. See Rashi's explenation. Rav Hai Gaon had a different explenation that you might not have access to so I'll quote it in short.
A fox tricked a lion into a trap when he told him he would not suffer for his attempt to eat a sleeping person, only his grandchildren would suffer. After getting trapped the lion complained 'but you said I wouldn't suffer?' To which the fox replied 'this is the punishment due for your grandfather's sin!'