This app was mentioned in 5 comments, with an average of 1.40 upvotes
Doing an overlay after the pictures are taken would be easy. Look at photo editting or other art like programs like photoshop, but for mobile.
As for an overlay while you're taking a picture, I'm not sure. I've never worked with mobile cameras. But a google search shows me how to create overlays in Android, and I recall an app that creates cutesy overlays (Snapchat I think?), so it must be doable.
I'd suggest looking more for camera and photo editting like apps and ignoring the fitness/weight loss aspect entirely when you're searching for an app. Unfortunately I don't know of an app off the top of my head.
EDIT: Will Overlay Camera work?
I can't believe there isn't one. The closest I found is one called Overlay Camera. You can choose a photo that appears when you use the camera. But, it's intended to mix the photos. Though, it has a mixing slider--so when it looks right, just make the old photo 100% transparent.
https://play.google.com/store/apps/details?id=jp.co.OverlayCamera.android.app.quick
You want an overlay photo app.
https://play.google.com/store/apps/details?id=jp.co.OverlayCamera.android.app.quick&hl=en
I didn't try it, but this looks like what you're searching for: https://play.google.com/store/apps/details?id=jp.co.OverlayCamera.android.app.quick
https://play.google.com/store/apps/details?id=jp.co.OverlayCamera.android.app.quick
Install that and just open an image of a perfect circle in the app.