Before revision:  It is known that it requires \Omega(\log\log n) time for queries provided O(n\mathrm{polylog} n) space is available and weights are from [0..n], where n is the number of tree nodes.
After revision:  It is known to require \Omega(\log\log n) time for queries provided O(n\mathrm{polylog} n) space is available and weights are from [0..n], where n is the number of tree nodes.