Feeling of friction on back wheel. Wheel nuts on too tight? The bike is an Avanti Discovery 8 which is a hybrid with a 8 speed Shimano in-hub gearing system.

The problem is I feel like there is definite friction on the back wheel. Spinning it freely it just doesn't travel as far as the front wheel and pedaling feels slightly impeded.

Obviously, brakes are easy to check and they're fine. There is no noise whilst coasting either, so I don't think it's the bearings.

I was wondering could it be something to do with the wheel nuts being too tight? I had a problem recently where the rear wheel was moving forward slightly causing slackness in the chain. I'd fix it, but it would keep happening so one day I really tightened it as hard as I could (the slack chain had come off causing me to crash).

Could this somehow be putting too much pressure on the hub?
Torque on the axle nut won't cause this per se. Think of each axle nut pinching the dropout really hard between itself and the hub locknuts. On a typical hub, if the locknut were loose against the cone, and/or if the axle threads were poorly lubricated, then tightening the axle nut can cause the axle to rotate relative to the cones, ruining the bearing adjustment and adding a bunch of friction. Shimano internal hubs with their burly anti-rotation washers are normally immune to this though.

Front wheels generally always spin way more freely than rears. All the Shimano internal hubs are somewhat on the draggy side. If you're noticing it when pedaling, make sure the chain is lubricated.

Things that could cause it to be worse than normal: poor hub bearing adjustment, need of internal lubrication using the special Shimano oil bath, dropout alignment causing excess bearing friction/wear, bent axle, something physically rubbing against the hub/wheel/tire, and brake rub.