I have pulled infinitive amount of weapons and I spend more time than most players in D2 and I can tell you first hand that Perk Weighting is widespread.
Example: I can go to Drifter and pull 10 Bygones and most of them will have the same perks on them when I pull them back to back, a lot of which are almost identical roles and since the perk pool for Bygones is so saturated the chances of them being like this is like hitting the lottery.
I know you guys have said that you are looking for a fix for Perk Weighting but please make sure that you look into all weapons because this is happening at everything from Vendors to Tonics to Dungeons.
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I love this whole perk weighting thing. Its all purely confirmation bias.