During my time in towers it didn't matter to me and as far as I know to anyone else. There are a number of sources of weight category available. It's on the strip, paper and electronic, displayed on the surveillance label for the target and just looking out the window. Most internationals are heavy so there is a prompt there. Although the weight category may be passed to the SMC, it isn't to the ADC. The ADC will scan available sources when deciding whether to line up/clear following aircraft.
When trainees are passing through the Learning Academy, there are enough "traps" in the simulator exercises to reinforce scanning. Once in the field the OJTI will be watching like a hawk, too much paperwork otherwise. After being rated, you possibly only ever miss a heavy once and never forget the experience.
Wake turbulence is not related to heavy aircraft only, it also applies between light and medium aircraft where the only cue is from scanning.