My physics is a little rusty but I would not think this to be the case. Gravity on Earth is more a manifestation of the Earths rotation(spinning on its axis) than it is the Earth's revolutional speed. Although I'm sure that the results of a slower revolutional speed would be catastrophic in any case.

Please learn to use the shift key. ALLCAPS is harder to read. Weight is essentially frustrated gravity. The Earth's gravity tries to pull us to it's centre, but the Earth's surface prevents us from falling in. It is this pressure on the Earth's surface which is weight. It is the force required to stop something falling. The Earth is free falling about the Sun - there is no surface stopping it fall so there is no weight on Earth due to the Sun. If the Earth were stopped and held on a big sky hook, there would be weight due to the Sun, but at this distance the force due to the Sun is much smaller than that of the Earth, you would essentially weigh a little less on the Sun side than on the dark side of the Earth. Tides are another thing though. Tides are due to differences in gravity and vary as the inverse cube of the distance. The tides due to the Sun would be eight times greater if the Earth moved twice as close to the Sun. Currently the Tide due to the Sun is 46% of that due to the Moon. The tide would become about twice that of the Moon making tides two and a half times bigger than now.

Motion absolutely affects gravity, but as Ragnarok said, it's primarily rotational, not revolutionary, speed. But yes, motion does affect gravity. It's general relativity. That's a part of the reason why as things increase in speed it takes more energy to increase their speed even more. I'm really bad at explaining the formula on this one. I tried to type it a few times, and couldn't make it make sense. But it requires infinite energy to reach C (the speed of light) because of this.

Here is what a Detroiter thinks: think of a yo-yo on the end of a rope: as the speed slows its outward force-or centrifugal force lessens-resulting in ambient drift that results in a gravitational increase-without the speed to lessen this effect (your at Cedar Point in one of those spinning do-dads and as it slows you fall to the ground). In reverse think of the Shuttle when it leaves Earth-it must reach a speed of 1/8 the earth's orbital speed to break free-or there abouts. If it does not it is trapped within the ghost of the machine-smiling... Seriously, here is a heavy question, if the earth's orbit slowed as you postulated-what happens to the oceans-do they empty out into space-I argue that it is the revolutionary speed of the planet (6.67 miles per second) that mechanically helps keeps the water at bay. If the water does not spill out and it overuns the planet-catastrophic in any sense either way-then at what temperature would earth have to reach for the entire ocean system (the pacific and atlantic in the main) to boil? That would be a lot of steam released into the atmosphere....I guess the umiverse would be taking a bong hit! LOL This would be hell on earth! Whew-its getting hot in here!