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If they're holding on to you and not the bike then it will be like this. Some bikes worse than others for slippy seat and no grab handles. It can help if they can get one hand on the back of the fuel tank to brace themselves against that rather than all their weight on you. You can also get some stuff called wonder web for the pillion seat that makes it really grippy so less sliding.
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More advanced pillion techniques help with this. One of the best for pillion and rider is pillions hands on their own knees, they can use their thighs to keep themselves back on the set and it's easier for the pillion to balance their weight. Thing is you need to lean with the rider to steer the bike in the corners so it's easier if your pillion feels comfortable with that feeling.
It's quite nice to ride really slowly if your pillion is all over you, build their confidence slowly. You'll miss the day when they felt the need to be hugging you so tight. :)
As far as noticing a pillion I would say I normally do, there have been times on long tours where they get involved and the weight disappears but generally I notice that weight on the back.
Took Mrs Hammer as a pillion for the first time today, which went ok (no-one fell off) but I hadn’t anticipated how much a physical workout it was going to be. Breaking/downhill especially!