Tidal amplitudes roughly scale inversely with distance to the fourth power (this comes from the tidal force scaling as r^-3 and the Earth's potential scaling as r^-1). At its formation, the Moon was approximately 7 Earth radii away from Earth, or about ten times closer than it is today. Thus, the amplitude of the tide on Earth would have been approximately 10^4 times larger than it is today. As the typical ocean tide is 1 m, this means ocean tides would have been 10 km high on Earth! Of course, the collision that formed the moon turned the surface of the Earth molten, so really we're talking about a 10 km tall molten tide, which is far less scary...(kidding).
Imagine all the noise the ocean makes when it crashes on a beach. That noise requires energy to produce, and is partially driven by the action of raising/lowering the ocean via tides. Now imagine how loud a 10 km wave crashing would be. This is why the Moon receded quite quickly from the Earth shortly after forming, the tides enable the dissipation of a lot of orbital energy.
As for the hypothetical effect of this supertide on the present-day Earth's weather, the Earth's troposphere (which contains pretty much all of the Earth's weather phenomena) extends 10-20km from the ground. Considering the height of the ground is changing by a similar amount due to the tide, I would imagine the effects on the weather would be quite dramatic.