We have heating pads that turn off on their own after a while (maybe 15 minutes?) which is a good feature.  Then they are covered with a waterproof material.  We use  towels or blue chuks on top of that.  We then take a small velcro tape-like fastener (maybe it's used in film or video work) to fasten the cord to something (a bar on the scale in our case) in such a way that it is not pulling on the scale.  Where you would fasten it would depend on your set up.
I have worked other places where we just positioned the heavy part with the on/off button and part of the cord cord on the counter top in such a way that it prevented it from pulling on the scale.  
Then you zero the scale and weigh the baby. 
It works great, is soft and cushiony and makes parents relax knowing their baby is warm.

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