To tilt or lean physically; figuratively, to have one's feelings, attention, or disposition move toward something.
強風で塀が少し傾いてしまった。
The strong wind caused the fence to lean a bit.
彼女に会ってから、私の心が彼女に傾いた。
After meeting her, my heart leaned toward her (I became attracted to her).
船が波を受けて大きく傾いた。
The ship tilted heavily after being hit by a wave.
To go down — used for the sun, moon, etc., moving toward the horizon (e.g., 'the sun tilts/sets').
夕方になり、太陽が西の空に傾き始めた。
Evening came and the sun began to tilt toward the western sky.
月が傾いて、夜の雰囲気が深くなった。
As the moon descended, the night's atmosphere deepened.
To decline or wane — used when momentum, popularity, or power decreases.
そのチームの勢いが最近傾いてきた。
That team's momentum has been declining recently.
時代の変化で会社の経営が傾いた。
Changes in the times caused the company's management to falter.
To tend toward a position or opinion — used when opinions or tendencies shift in a particular direction (e.g., public opinion leaning one way).
最新の世論調査では支持が野党に傾きつつある。
In the latest polls, support is starting to lean toward the opposition.
議論は賛成に傾いたが、まだ結論は出ていない。
The discussion has leaned toward approval, but no conclusion has been reached yet.
彼は最初は反対だったが、徐々に考えがそちらに傾いた。
He was opposed at first, but gradually his thinking inclined that way.