Fetching details from the dictionary...

tender; warm; caring; thoughtful
meticulous; detailed; attentive
deep (of a colour); thick (e.g. fog)
「細やか」 has another reading with different meanings.
細やかな気配りができる人は周囲から好かれる。
People who can be considerate in small ways are liked by those around them.
彼女の細やかな心遣いにいつも感謝している。
I always appreciate her attentive thoughtfulness.
細やかな心遣いに感謝した。
I was grateful for the thoughtful consideration.