It's pretty simple really - they just change the MTOW according to the required load. For example. If the ZFW weight is 58 tonnes and you need 6 tonnes of fuel then you can go 66.9. It's quite common to do a whole 4 sector day at 66.9. Longer trips like UK to Canaries will typically require 74.9. If you need more fuel then you just up the weight to 69.9 or 74.9 as appropriate. Requires a little bit of thought at the crew room stage but its not a big deal and I believe saves the company significant sums.
At the moment only engineers can change the weight placard and the tech log but Captains will soon be authorised to do this.