SteveG has basically said it all!
Grease the 2 nipples that hold the spring at the back of the arms!!
This will allow the arm to move more freely up and down the spring. If the spring is moving freely on one side but is sticking on the other then it will pull one arm in quicker than the other!! Check the nipple grooves are smooth from paint and other crud and grease them like the proverbial pig!!
Make sure you have the correct washers between the arms on the spindle bolt.
Some are plastic and others are metal. I'm not sure which came with the 1000's but I think they're metal.
Greasing these should help too!
Dont overtighten the spindle bolts nuts at the front!! They should be tightened against each other so that they dont come loose but they shouldn't be tightened against the arms as this will restrict the movement. Similar technique to 1 pc cranks to stop them coming loose!!
Front two nuts tight against each other and the back nut tight to stop the spindle moving. The spindle should be centred based on the integral spring housing. The spring can be moved to help centering but it can't be moved very far. So centering the spindle first will give you a good place to start.
Have you tried moving the spring all the way to the other side to see if it swaps the sticking arm to the other. If it does then you just haven't centred it right.
Make sure all moving parts are greased and are free moving.
Make sure you dont grease ya pads though!!
Check your wheel is centred too!!
If its slightly to one side then add/remove washers to pad it out on both sides to get it centred.
As SteveG said. A piccy will help diagnose. If the brakes were bought used then explode the parts. Maybe your missing a washer that goes between the brake arms or summat!!
Thats it!! I'm all out of ideas!!