We have a blue bin for paper waste (no cardboard). It's the size of a small wheelie bin and I usually put that out once every 2 months. Sometimes I can go for 3 or 4 months without putting it out - depends how much cr@p gets put through the letterbox.
We have black boxes the size of large stacking boxes. These are for glass, aluminium, steel, plastic bottles, aerosols, and clothing. I tend not to put clothing in very often as I put that in charity bags instead. I have two of them* and they are collected fortnightly. One's always full, the other's sometimes full, sometimes only half full depending on how many bottles of lager DS has had.
The 'big' bin used to be full every week, but these days it's not usually more than half full. LO has refused to wear reusables since she learned how to unfasten the velcro herself, and she refused to walk in them anyway. So we're on disposables, which are down to a couple a day. That's really reduced the bin-load. I have to shamefully admit that last time the bin was emptied it was nearly full

because we had take-away pizzas one evening (which came in 6 boxes), then on my birthday a few days later, OH and I went for chips at seaside and the kids ordered more pizzas - another 4 boxes and they can't be recycled here.
*actually I have four. The Council gave us one and I said it's not enough and need another. So they sent me another one. Then another one. Then a neighbour decided to dump theirs on us when I wasn't looking. They are so useful I'm not complaining. I keep one in the greenhouse to keep compost in, and with the lid on top I can store things on the top. The other one gets used for putting weeds or rubbish in while I'm gardening.