Magic: the Gathering has pads of paper with 3 columns divided into 2 each, to allow one player to keep track of life for both them and their opponent. You may want to do something similar with your opponent's live points in yugioh. Both of you aren't infallible of course, honest mistakes could happen, at the recent MtG prerelease one source of life gain was missed a few times by my opponent, but when I pointed out where the difference was they accepted it. This is good advice to use for all your games, first it will not look like you are singling out one person, second, two people keeping track helps prevent those honest mistakes in other games where someone forgets to carry a 1 or misses writing down a source of damage or gain.
Looking at set cards and your hand should be easy to prevent, for set cards they would actually have to touch and look at them, for your hand they would either need to stand behind you or again touch and look at them. Both are things that you should easily be able to spot. As for removing of counters, this should be fairly easy to spot too, they have to actually take them off the card.
If you are having a hard time proving this player is cheating, perhaps have an outside third person watching the game, someone not focused on playing it (like you are) looking only for the cheating you suspect. This would work particularly well if your opponent doesn't know about it.
If this is a competitive play environment, there would be a judge or a TO this can all be reported to, if it's casual play, there really is no recourse, but then, there is no stake in the game either.