Hey, Tamara,
Well, if it's light, it will never be totally all-errain capable. Lower weight makes for a flimsier chassis and can be prone to getting loose. And a parent-facing seat makes it even harder on this - that feature itself adds to weight quite considerably, and a light reversible pushchair already will have to be stripped down of a lot, especially terrain-capability-wise.
Personally, I will recommend the Cybex Eezy S-Twist+² which is compact and reversible but simple, while having a tad larger wheels. I think that could be your best bet for traveling with a parent-facing pushchair which doesn't have tiny wheels.
I would, otherwise, recommend the Cybex Mios which has small wheels but is sturdy but light, and reversible as well. Or just looking at non-reversible strollers that will offer more space/wheel options with a lower weight.