Here are some proverbs you can read with kanji from the first 10 levels.
Readings and meanings are blurred so you can try reading and understanding them before revealing them. It worth noting, though, that some of them use classical / literary grammar, which may be unfamiliar to even intermediate learners.
This list isn’t exhaustive. I might post more later.
Meaning: perseverance prevails; three years on a (cold) stone (will make the stone warm)
Meaning: if you do a favor for somebody, you will get a return favor; if a fish is friendly toward water, water will be kind to the fish too; mutual back-scratching
Note: this one has a reading for 魚 that isn’t taught on WK
Note: 魚心 can be used independently of this proverb as a reference to it
Meaning: No child understands how much they are loved by their parents
Meaning: a journey of a thousand miles begins with a single step
Note: this uses a meaning and reading for 里 not taught on WK
Note: a 里 is an old Japanese unit of distance roughly equal to 2.5 miles or 4 km, but 千里 is used to mean “a really long distance” and not necessarily anything specific
Meaning: Time is money
Note: WK teaches the word for money with the honorific お, but here it’s used without it
Meaning: not giving up; keeping at it until one succeeds; falling seven times, getting up eight times
Note: 転 is a level 10 kanji, but the word 転ぶ, where this reading is taught, is in level 12
Meaning: what happens twice will happen thrice
Meaning: good talkers make good listeners