I get your point, but please, do understand there's NOTHING inder 7 kg that would be comfy on cobblestones. YOu need big wheels & sturdy chassis meaning higher weight. Cobblestones are a serious strain so the "bulkier" the better the properties while driving!
Moving on, I would, therefore, suggest something around 7-8-9 kg to suit you. My own preference here would be an Oyster Zero as it is light (a bit over 7 kg), with super large canopy coverage, a very wide seat (I could put two sons at the same time inside) and is WILL last you. It will NOT be an all-terrain beast with this weight, though.
My next suggestions would include a TFK Dot 2, a Baby Jogger City Mini2 (yes, this one can get a bit expensive some places), and similarly sized pushchairs. Only those will REALLY be able to accommodate a larger heavier toddler (as opposed to super small ultracompacts that only can do that ON PAPER, IRL they get too small for larger kids...
Hope I helped!