This is the 439th most frequent Japanese word.
っぽい
"-ish" or "seems like."
The usage of "っぽい" here conveys a resemblance or characteristic feature typical of children, indicating that the clothes have a design similar to something a child might wear.
彼の服はいつも子供っぽいデザインだ。
His clothes always have a childlike design.
In this sentence, "っぽい" describes an impression or quality that resembles spring, giving the sense that today's weather shares characteristics associated with spring.
今日は春っぽい天気ですね。
Today's weather feels like spring.
Here, "っぽい" refers to a tendency or propensity, indicating that the actor's face appears to have a characteristic of easily showing tiredness.