She's been putting on weight lately.

Literal

She [topic-は] lately fattened-came.

近頃 ('recently, lately') is a slightly old-fashioned alternative to the more common 最近. 太ってきた combines 太る ('to become fat, gain weight') with the auxiliary ~てくる in its 'change-over-time' sense — capturing a gradual development that has reached the present. The pairing ~てくる + change-of-state verb is one of Japanese's elegant ways to express trajectories: 寒くなってきた ('it's been getting cold'), 慣れてきた ('I've been getting used to it').