How to win with a “weak” Knight?

Perhaps the Beaver Castle is the easiest to build.

Very debatable!
I believe the Warlock Castle is the easiest to build, because the Centaur Gargoyles and Griffins are enough in the first two weeks to break through all ranged blocks, even such as the Lotus Grand Elves, while the Barbarian can simply lose against such an army, even with Trolls!
And against flying units, Hydras are simply ideal; against slow-moving ground units, you can use Hydras + Centaurs, protected by a few Gargoyles.
If you can't build Hydras in the first week, then go for the "economy" (underground +500 gold) and possibly the 2nd level of magic.
But in the second week, you need to start building Dragons.
At least Dragons are not much more difficult to build than Cyclops, Paladins, or Phoenixes - but the effect they have is simply overpowered.
Of course, the tactics and construction will differ depending on the richness of the map and the opponent, but the general principle remains - 1-3 monsters at the start fight preferably against magic, until the Dragons appear - and then you can open 2, 3, or even 4 fronts...
P.S. So, the "weak" Knight has a chance only at the Slugfest, and even then, not against the Sorceress.