This article deals with common social problems， with much attention being paid to problems of teenagers.

我们把这句还原一下得到如下：

This article deals with common social problems.

Much attention is being paid to problems of teenagers. 其中is being paid to是被动语态的现在进行式，其表达的动作性很强。上下两个句子结合起来，形成带伴随状语的复杂句。那么，with...being done的形式被保留下来加强动作的描述。

而第二句：

He lay on his back with his teeth set and his eyes closed?

只是表示一种普通而稳定的状态，正在发生的意味不强，故没有加being。