Gimp and blender can do similar things.
Gimp is like a free photoshop, so it is not like an animation thing, but it kinda has animation support. Mainly, it breaks down animations by frames and save them as different files or something, or layers, and because layers can be anything, I think if you rename some files you can have it automatically load in your files (after renaming all 1000) and apply the same effect. Well almost. I am not confident that this is how gimp work (but I think I have tried similar tricks in the past) but gimp is not a dedicated animator so it doesn't do complex operations, in fact it can hardly do anything, sure you can make an animation and add effects and filters, but if you want it to do something, like interpolation, and render out an animation, that I think is still a bit too complex for gimp, as it can't automate certain animations, like movement and fading. that is more like, you edit yourself.
Now blender could possibly do that, the issue is you kinda have to be technically skilled to used blender.
You can make a mesh for the image, and a shape key that makes the animation of going up and down, and another for the belly change, you can animate these behaviors. not sure if it is what you want. But then on top of that (you pretty much have to make a basic shader any time you use blender, but it uses nodes so no coding), you have to make a shader that, is able to set what image it uses. you then tell blender not only to animate the character and the changing belly (I believe there is an animation layering system that will help make this easy if you want to animate, change the belly, animate again, and slowly change the belly shape after each run through the animation), but to also cycle through the different characters. Two issues is, as a first mentioned this is a rather technical process that kinda takes a good amount of experience to do, not that it is hard but researching all the steps is going to be the death of you, not that there are a lot, its more like, never knowing where to start, or what you can do, so you don't know the right questions to google. the second issue is that, at best blender can render out all of these images for you, but it will at best render each animation as one big animation, you will still have to cut it up into their unique parts, and infact, you have to first render as individual images, and then animate the images as a collection, blender could do this but you may also use your own favorite program to stitch the images together. idk, the whole process may be a bit too complex for any one program to do everything you need it to do... unless... well I guess what you could do is, in blender, you can do is, if the animation does work out how you want it and get the style you want and you are ok with it, so you for sure want to render out a batch of characetrs and stuff, doing a python script (can be done inside of blender) using a for loop, maybe too, and it can not only cycle between all the content you want, it can make all the animations and sepratet them out for you. but as I have mentioned, this would be a bit technical, requiring the additinoal programming knowledge of both python and blenders api. I am not the most familiar with python so I can't say much but I do use other programming languages and I have dabbled with blender scripts. But all of this could be more work (especcially if you want to learn how to do it on your own) than just beating your head against the wall trying to do all 1000's.
If you do want to consider the blender option, but are not familiar with it, and you don't feel confident about using blender without maybe some guidance, what I can do is, I could help you see if we can recreate the animation and the effect in blender, see if it meets your expectation, and if it does, I can go about learning how to automate everything for you. If you are willing. I won't be able to know for sure if blender can match the animation you were getting out of your previous program, so if you do want to explore this option, i may be asking a lot of details about not only what the animation entails, but similarities and differences between all the other ones you want to do. IE are all the characters the shame shape? If not, can they be catagorized by shape or body types, I ask because this will only work if all the characters have similar belly designs, because my shape key suggetion is like a type of warping effect, the warping applies to the mesh, not the image, the image is just applied to the mesh, and if the image of the characters have different bellies then the warping will not work for different images if the belly isn't being warped the same. Most automation only works if things are exactly the same, or somehow contains data with it to explain how to properly process it.
