Not all full-frame digital cameras are dramatically bigger or heavier than comparable 35mm film cameras. A fair comparison is between similar classes of cameras: professional film SLRs with motor drives and batteries can be close in size and weight to pro digital SLRs. Examples given in the answers show film and digital bodies within roughly the same weight range.

The biggest difference is cost and complexity. A film camera body mainly needs to be a precise light-tight mechanism that holds the film flat at the correct distance. The light-sensitive recording medium is the film itself, which you buy separately each roll.

A digital camera must permanently include the expensive part: the full-frame image sensor, plus processing electronics, buffer memory, storage interfaces, power management, and a rear LCD. Those are high-tech components built to extremely fine tolerances and add both cost and some bulk.

So the main reasons are:

• the sensor is costly and technologically difficult to manufacture
• digital bodies need substantial electronics and display hardware
• pro bodies often add grips, batteries, and extra features that increase size

Cameras have improved over time with lighter materials and better integration, but digital full-frame bodies can’t be as cheap as basic film bodies because the image-capturing medium is built into the camera.