The proposal is intuitive and appealing. It appears predicated, though, on the implicit assumption that high-rep people provide better information than low-rep people about the quality of questions and answers. This appears derived from equating reputation with knowledge, capability, or capacity for judgment. That equation is debatable.
(On our site there are users with enough reputation through sheer activity alone to have earned tag badges in subjects where they are not very knowledgeable. I will, with some diffidence, hold myself out as example number one: purely because many questions are tagged with r, I earned a tag badge for r before knowing enough about that software to even offer an R-based answer to any question! On the face of it, then, my votes on R-tagged questions and answers ought to count less, not more, than those of experienced R programmers.)
A deeper concern I have is that differential voting power could create an insular clique of high-rep people who effectively control the scores of questions and answers. I worry that this could narrow the site to reflect only the interests of its most active users.
When proposing significant changes to how this site works, we should always ask ourselves, what higher purpose would the change achieve? In this case, would we attract or retain more users? Probably not. Attract high-quality users? On the contrary, such people might be put off by having relatively little influence despite attaining demonstrably high levels of expertise. Improve the ratings of questions and answers? Perhaps--although that depends on assuming reputation (which measures activity) reflects the capacity to judge quality, as I discussed in the opening paragraph.
An interesting way to pursue the original idea would be to implement an alternative reputation/score measure in parallel with the existing one. At first this could be done invisibly and experimentally (by making the measure visible only to a few experimenters). If at some point evidence arose that the alternative were beneficial, then the alternative scores could be displayed to the world.