Sympathy n. 同情(心);同情;(感情上的)支持

I have great sympathy for people in affliction. 我对那些受苦受难的人们充满同情。

His wretchedness aroused our sympathy. 他的不幸激起了我们的同情。

Let me convey my deep sympathy to you. 允许我向您表示最深切的同情。

I show my deep sympathy to you for what you’re suffering. 我对你遭遇的这一切深表同情。

I have some sympathy with that point of view. 我比较赞成这种看法。

sympathize vi. 同情，支持

I know you feel angry, and I sympathize. 我知道你感到愤怒，我也有同感。

I sympathize with you; I’ve had a similar unhappy experience myself. 我很同情你，我自己也有过类似的不幸遭遇。

He could neither understand nor sympathize with my eagerness. 对于我的急切心情，他既无法理解也不能体谅。

I really sympathize with your sufferings. 我对你的痛苦表示真诚的同情。

I sympathize with you from the bottom of my heart. 我打心底里同情你。

总结：

Show / convey sympathy to somebody for something

Sympathize with something/somebody

Oh, poor man, come on, let me give you a hug, I sympathize with you from the bottom of my heart. Please take my sympathy for your sufferings. Loss of 2 dollars is not that bad, here’s my 5 dollars. 可怜的人呢，过来，让我给你一个拥抱，我从心底里同情你。请接受我对你的痛苦的同情。丢了2块钱也没那么糟，这是我的5块钱，收下吧。