Make it thicker!
For illustration purposes I found two (blank) PCBs of differing thicknesses - one is (tinned) double sided 1.6mm thick and the other a 4 layer board (from an old project) that is 4.0mm thick. Both boards are approximately 300mm wide. Clamping both in the vice, I pulled...
(and what you can't see is that I'm pulling
*much* harder on the 4.0mm board!)
And a picture tells a 1000 words...
(I'm sure beam deflection formulae (
https://en.wikipedia.org/wiki/Deflection_(engineering)) would yield a far superior scientific approach to deciding how thick a PCB you need, but you get the idea