At checkpoints, a guard lights a standardized candle and puts it in a tamper-proof holder and seals the lid with a wax seal. Illegal possession of the seal and of similar holders is a serious offence, obviously.
At further checkpoints, the candle is inspected and if it isn't exhausted, a fine is levied. A new sealed candle is provided for the next stretch of road.
However, I think we need to step back a bit. Foot traffic is unlikely to have enough of a spread of speeds to be an issue, unless there are runner-messengers whom you wish to discourage (which you'd have only if horses weren't readily available). Heavy drayage is also likely to be pretty much uniform in speed. The faster traffic will be light carriages pulled at a trot, and fastest will be riders galloping, like the pony express.
So if the goal is to raise money while reducing speeds, a tax on the faster modes would be more apt: one level for light carriages and a higher level for riders. A permit would be issued, which would need to be displayed.
Or, a law fining people for running their horses or themselves in modes faster than a walk (which can be well-defined in both cases), enforced by observers along the way. I believe historically some towns had bylaws against galloping within certain areas.
It's really only with the advent of motor-cars did we get the capability of moving at speeds twice or three times what we want to allow.
