Static is a pain in the can for everyone. Gunpowder manufacturers put graphite on the exterior or the powder grains to make them conductive, and keep the grains from going off. Try wiping the plastic tray or plastic items with a damp washcloth with a little dishwashing detergent in it. This will eliminate the charge in place, and may event prevent a new charge from building. You might try wiping the tray with some graphite lubricant powder. This will make the plastic tray conductive. You might have to coat both sides. I'm not an 'expert' but that's what I'd do. You want the static to be able to find a path to a ground. You can buy an anti-static mat at a computer store which has a wire which can be attached to an electrical ground. You can put your scale on the mat and it will keep you and the scales grounded.
If you really are serious you could raise the humidity in the room, and buy an anti-static machine, which has a fan which blows ions out to neutralize static charges.