The HAARP facility will not affect the weather. Transmitted energy in the frequency ranges that will be used by HAARP is not absorbed in either the troposphere or the stratosphere - the two levels of the atmosphere that produce the earth's weather. Electromagnetic interactions only occur in the near-vacuum of the rarefied region above about 70 km known as the ionosphere.
The ionosphere is created and continuously replenished as the sun's radiation interacts with the highest levels of the Earth's atmosphere. The downward coupling from the ionosphere to the stratosphere/troposphere is extremely weak, and no association between natural ionospheric variability and surface weather and climate has been found, even at the extraordinarily high levels of ionospheric turbulence that the sun can produce during a geomagnetic storm. If the ionospheric storms caused by the sun itself don't affect the surface weather, there is no chance that HAARP can do so either.