As I see it, the strongest evidence supporting such a link includes:
1. In most large, epidemiologic studies, uric acid is a clear risk factor for developing hypertension; furthermore indigenous cultures with low uric acid levels (probably due to a non-Western diet) have low incidences of high blood pressure.
3. Making rats hyperuricemic induces hypertension due to a mechanism involving a direct endothelial toxic effect of uric acid.
There are certainly caveats to this hypothesis--for instance, rats aren't humans, epidemiologic evidence does not imply causation, and a large randomized controlled trial is really necessary before we should be using allopurinol as a blood pressure lowering agent. But it's an interesting story thus far and if it's true, it could really impact one of the most important public health problems which exists.