Reinforcing sagging shelf

[Brigadier]

It appears to me that you'll always be trying to make a silk purse from a sow's ear with this.

But, if you insist, a good start would be replacing the

flimsy plywood

cupboard backing with 12mm ply, or similar: this will add a lot of rigidity to the structure itself, as well as better and more numerous fixing options (for the rear length of each shelf).

 

[JohnD]

Fixing battens securely and rigidly to the long edges of the shelves will improve beam depth and thus strength and stiffness.

The battens must be tightly fixed with glue and multiple small screws or nails. The battens should be on edge to maximise height.

The back edge is out of sight so you can use a larger batten, and/or one on each side.

If they have already sagged, turn them over and it will work even better.

 

[mrrusty]

Shelf reinforcing with painted mild steel square section and furniture connection screws (they go right through, and the heads are slightly recessed in to the top surface). You only need two screws - one each end. The shelf bending is resisted both by the rigidity of the steel tube and by the fact that it is in tension (it would try to be stretched if the shelf bent downwards). Neat, and it works - done it loads of times.