neck size is slightly more beefy than any other Japanese 335 copy eg. Tokai. It is not baseball bat thick but somewhere inbetween a 50s and 60s LP. Weight wise, they are a tad lighter than their Gibson counterparts.
I just got one of these last month. The description is between a 50's and 60's neck. I think that is about right. I do not find it as thin as say a 60's les paul type neck, but its not as thick as the 59 LP replica type of neck I have either. If it was closer to one vs the other, I would say closer to the 59 than the 60.