He is under a heavy debt.

他负债累累。

《新英汉大辞典》

His father died, leaving him in heavy debt.

他父亲去世，给他留下大笔债务。

youdao

She bought whatever she liked and ended up in heavy debt.

她喜欢什么就买什么，结果负债累累。

youdao

Many banks,he says, are going to need additional capital to deal with bad loans and heavy debt.

VOA: special.2009.05.29

It involves loans, debt guarantees and other support to euro area countries with heavy debts.

VOA: special.2010.05.14

That would be good news for European countries with heavy debt loads.

VOA: special.2010.05.07

He was also in heavy debt to others and feared the bank would reveal them.

BBC: Bedford knifeman Barry Bell guilty of stabbing colleague

Now, it has such heavy debt that the home islands may sink under the weight of it.

FORBES: Dire Consequences As Global Growth Grinds To A Halt

Transocean has been struggling with a heavy debt load that has put pressure on its credit rating.

FORBES: Transocean Forgets Macondo, Focuses On Offshore Market Strength