I came across the sentence which reads 以色列宣称要让哈马斯付出沉重的代价.
Heavy cost is no problem in English, but cost or price 代价or 价格 in Chinese often comes with high or low, not heavy or light, so am I right to say this is a word-for-word translation from a set phrase of English or other European language, like the most well-known "armed to teeth", which is made "武装到牙齿" and accepted by the Chinese readers?
but cost or price 代价 or 价格 in Chinese often comes with high or low, not heavy or light,
Heavy or light is often used to describe "loss"(损失), the 代价 in 沉重代价 refers to 作为代价的损失 (loss as price) and that's how we understand the meaning of 沉重的代价
We usually don't translate English expressions word for word when there is an equivalent idiom in Chinese. For example, we don't translate "at the end of one's rope" literally as 在他绳子的末端, we translate it as 山穷水尽，穷途末路， or 走投无路.
Another reason to translate word for word between English and Chinese is the literal translation is easily comprehensible. for example "an eye for an eye" --> 以眼还眼
Translate "arm to teeth" as 武装到牙齿 is acceptable only to people who know this English expression. It is not an easily comprehensible term for the general public. 极度武装 would be an accurate translation
Using heavy to describe price is nothing unusual. Before the introduction of paper bills, large sums of money are paid in gold or silver ingots and measured by their weight. Hence words like 千金 (1000 liang of gold), 重金, 重赏, 重禄, 重酬 etc., all expressing "a large amount of money" using "heavy".
The word 重价 is attested in late 18th to early 19th century.
近代汉语大词典 p.2415 on the word 重价:
The word 代价 is translated from Japanese 代価. It seems to be introduced rather late. It is plausible that "沉重的代价" is word-to-word translation from "heavy cost", but in any case it is not a new sense of 沉重.
In general, cost means money. Money equals gold in the past. Gold is measured by its weight, not counted by number of dollars. That is why we can understand "heavy cost".
In Chinese, it is OK to say "沉重的代价", which means that you will pay back with a lot of gold, if not with your life.
We often say, "重赏之下，必有勇夫"。In ancient, the Emperor granted its warriors a lot of gold and silver, fields, slaves, and livestock. Those are called "重赏".
