Look into the several cardboard stools which are commercially available.
And read the limitations on those as far as weight is concerned.
A google images search 'cardboard stool' will reveal many stools and several chairs.
This link leads to a stool on a commercial site, very basic two sheets of cardboard crossing and a third sheet on top as seat, they rate it to 150 kg (330 pounds), and adults rather than just kids.
If you have plenty cardboard you can do a couple of tests with heavy weights but as long as you have the card board in its strongest position (vertical) and with enough body (thick corrugated board or folded and used with more fields thinner corrugated boards) you will be good for your weight limits.
As far as I remember a box as people use to move house will rate about the strength when just folded shut, adding tape or glue to fix the shape will add strength and you might be able to cut away part of the sides opening up the structure.
An other approach would be to stack cardboard, any kind, to the needed height and use that for the base. Cutting out parts of the sheets will give the impression of legs while still keeping enough strength.
Commerically made cardboard tubes will be strong enough for a chair, even fairly thin ones, but the problem will be how to attach them to a seat or frame for the top of the chair.
In work we use the stretch wrap film that goes around pallets when loaded and that comes on tubes of about 2"(5 cm) diameter, about 20" lengths (50 cm) (From memory, might be off a bit) and those will make sturdy legs if you can fit them into your frame or seat strongly enough.
Those tubes should be available from any company near you that wraps their loads.
Just using glue to attach a tube to a plain flat field of cardboard is likely going to result in a failure while using or even already in the building stages.
You are more likely to get it working when you carve a connection out of the cardboard of the seat or build up a core where the tube/leg slips around.