Hi, Roberta,
Well yes, you cannot possibly put large wheels and large anything else (like the canopy) and have a stroller under 8 kg that would not be totally rattly and loose because of super thin bars to get that weight. Realistically, there's no stroller like that.
I would recommend going for a Baby Jogger City Mini GT2 or just the more urban Baby Jogger City Mini2, which are about 10 kg but will withstand more than a smooth surface in the mall plus a child of up to 25/29 kg). Or go for the Oyster Zero which has not all-terrain but nice enough wheels, HUGE canopy and is up to 20 kg.
None of them has, unfortunately, removable covers.