Because her son is interested in reading,she often buys books for her son.

用以下两种形式的独立主格结构，都正确。

Her son being interested in reading, she often buys books for him.

Her son interested in reading, she often buys books for him.

下面是针对分词作状语的解答，同样适合于独立主格结构：

1. 单个的形容词作原因状语，这时应加being，变成非谓语动词，即：现在分词。非谓语动词作状语非常自然。
例如：
Being ill, he can’t attend today’s meeting.
Being hungry, they had to look for food.

2. 如果是分词形容词（由过去分词变来的形容词），加不加 being 均可，因为它曾经是分词，本身就是非谓语动词。
例如：
(Being) worried about his health, she couldn’t sleep.
(Being) surprised at the news, he kept asking how.

3. 如果是形容词词组作原因状语，加不加 being 均可。例如：
(Beng) seriously ill, Tom couldn’t go to school.
(Being) sad over the news, she cried all day.

个人看法：语言追求简练，但也应避免单调。单个的形容词之前加 being，主要是为了避免单调。一个形容词读起来会非常唐突，像 ill 和 angry。若是Being ill，Being hungry 则很自然。