You can't have the stability and light.
If it is light, then centre of gravity will be high which in turn will not be stable. You can't have a 6kg camera on top of a 1kg tripod with 22mm column and expect that to be as stable as a 3kg tripod with 28mm column.
There are some middle ground but as a whole that is the general rule of thumb.
I have a Manfrotto 055pro, aluminium. It is heavy, I don't deny it. That thing will support heavy gear easily, it is stable but I simply do not travel with it.
I also just purchased a Redged 525k. 1.2kg. It's so light and small it fits inside my messenger bag. However, putting a DSLR on top it will be top heavy (even if it's strong enough to take it twice over). So you are just going to have to "make do". For me, travelling with something light is better than travelling with something heavy, especially if you are walking a lot. You can always hook things under it to lower the centre of gravity or hope it wouldn’t be windy for that 20 seconds shot.
There are other tripods that falls in the middle ground which is around 1.4 to 1.6kg that are not as compact and arguably more sturdy. May be they will suit you. At the end of the day, no tripod is perfect and it depends on what you value the most. If you are travelling by car a lot then I would get the most sturdy one. If you are on foot then I would get a light compact one.