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so you dont want to merge 1000 layers together you just want the 1 layer to merge to every other 1000 layers if it is going to be the same location you can record an action doing it and the use the file > Automate > Batch and choose that action however it will be quite strenous on your machine and may take some time unless you split the layers into groups. And of course this will only work on 1 image at a time so if you mean 1000 layers in 1 document it will not work essentially you need 1000 seperate images.

I am probably overlooking the obvious solution here but I cant think of an eay 1 click solution which does not include duplicating the image 1000 times and merging the layers. Or making 1000 layer comps