English Translation
His debts were piling up.
かさむ (or spelled as 嵩む in Kanji) is a great free translation.
We rarely say 借財 these days, though. 借金 (しゃっきん) is the synonym and it’s more common.
Technically speaking, 借金 includes only direct debts that you own to pay back in the future whereas 借財 can also include indirect liabilities (e.g. you are a debt guarantor for a third person, and when he fails in his pay-back, you shall pay on his behalf).