... this thread has responses going for about 4 completely different basses, and 3 other than OP is inquiring about ...
1) the MIM Classic Series 70's Jazz which OP is asking about (that seemed to have the most neck stability issues in the first couple years after introduction ('08), as bassman74 mentions)
2) the American made 70's RI's
3) the MIJ 70's (Japan had their own 'Classic' models, not to be confused with the MIM Classic Series)
4) and then the actual basses from the 70's ... many in nat ash and very heavy as mentioned
... just make sure you are comparing apples to apples