Tensioned leather saddles sag and "hammock" faster and to a greater extent than modern "plastic" saddles. This is simply because there's nothing but a thick piece of cowhide under tension to resist the sag. Modern saddles employ a plastic or CF frame to support the rider, with padding and leather or similar material on top. There's just more saddle in a modern plastic saddle to resist sag.

OP, you should avoid Brooks if you don't like sag, and prefer a flat saddle so that you can shift weigh forwards and rearwards to alleviate pressure points. I own Flite and B17 saddles, and the Flite is much better at resisting sag, and more comfortable long term. Brooks saddles are hard as a rock and uncomfortable when new, then they soften up a little and work pretty good, then soon after they start to sag, at which point they become uncomfortable and nearly useless to me.