Hi, Sharon,
Don't, please, expect your stroller to be lighter much than the Oyster Zero. I mean, it is about 7. kg and even ultra-compacts are sometimes heavier - or lighter by 200 - 300 grams. So the weight, you'll have to endure - the more so if the stroller should be carrying a 3.5, 15 kg toddler.
I actually wouldn't swap. You'll end up disapponted.
...But if you really really must have something even smaller, you absolutely need it to be sturdy enough - so cheap ultracompacts (more about them here) will just disappoint you. I myself would look at the Joolz Aer as that is a travel model with a high backrest, which is rare. I know, it is not cheap, BUT you can always get it second-hand and save money (and your nerves) instead of buying a cheap model that will shake and rattle and be impossible to push and after a few weeks fall apart - not even talking about a short backrest that will make your child's head falling backward). Still, this size of buggies is meant for OCCASIONAL use only, so count on a smaller stroller not to be very comfy anymore after it gets downsized in terms of seat, wheels - and everything else.
And, about the brake - read our cleaning and maintenance guide for stroller users and oil the brake a bit ;-)