To increase or accumulate (in amount, cost, burden); to mount up.
最近、医療費がかさむ一方だ。
Lately medical expenses have been mounting up.
荷物がかさむので宅配を頼んだ。
My luggage was getting bulky, so I asked for a courier.
忘年会続きで出費がかさんだ。
With one year-end party after another, expenses piled up.