I believe some animators like David Pagano of Paganomation prefer using spring clamps to hold down their baseplates.

Do you have a picture of your set or studio? Maybe the baseplate flexes so much because there isn't much built on the baseplate to weigh it down.

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I never animate directly on baseplates anymore.  It's not a very good way to go.

Instead, try building on top of the base plates with plates and bricks and such.

I do the same. I have found that it helps a lot.

Thanks for the tips.  I have a reasonably large set and i have a few wide shots and a long pan that would seriously tax my grey block collection. 

Options:

Continue tacking until the flexing stops;
Try a different plate to see if they are all "warped" (i have 4 plates);
Use a false floor as suggested and redo my storyboard with this limited floor space in mind;
Use a green base plate (thick)
Dont use any plate and set up directly on my desk;

Ill think this one over.  Hopefully option 2 works straight off.

To add on to what Pritchard said, if you have some couple-pound weights to weight down the baseplate (I occasionally use a pair of 3 pound weights). However, I normally use bricks or plates to build on the baseplate (what ANP said). The final possibility I've previously used is tape, although that can sometimes have some wiggle room still.

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Thanks for all the tips guys - I'm trying each suggestion one by one.  I tried the tack but I used too much and I had dips and valleys all over my plate - I used too much so it actually made the bounce worse.

I tried using two cans of soup to weigh down the plate.  That had some success but I then had the challenge of maneuvoring around these large tins of soup.  I used a bag of sugar - that actually provided a hand rest for me when doing fine movement.  I'm going to consider something similar in a permanent way.    I think a bag of rice or sand (that doesn't leak might make a great hand rest when doing fine head/hand movements.

Anyway - I then changed to two different base plates.  Here is what I got*:

https://www.dropbox.com/s/umms5fx0deiby … ttesta.avi

* shot during day, curtains open only one lamp on, put on a loop.

If you ignore the light flicker and focus on the background, there is a minor amount of bounce.  I'ts mostly noticable when the loop jumps from the end to the beginning.  My real vid won't loop - so I'm hoping that most noticable bounce won't actually happen for real.

I think I can do better with small amounts of tape and securing the camera a little bit more.