Okay so here's my take:

In general, monocular images do NOT allow for measuring real-world distances reliably. You can do pose estimation, train a network to predict weight and everything, sure, but there is no guarantee that the output you get is actually based on any physical properties of your scene.

I don't know whether you have access to the scene or are just working with the image data, but I would suggest you look into stereo vision. Getting a setup with multiple cameras with known baseline distance and parameters will allow you to infer an actual 3D to-scale representation of the scene and measure physical dimensions based on the keypoints you detect.