He went to work sick, and despite nasty weather.

He went to work sick.
He went to work depite nasty weather.
两个句子用and连接～

他开始辛劳的工作，不管多么糟糕的天气。

He went to work 后面的sick是补足语，表示处于某种状态。
例如I came home,tired
后面那句是补足语的并列结构，表示天气很糟糕。

他带病上班，并且尽管天气很糟
sick为形容词作状语
不要害怕这种语法
多读几个这种句子自然就会了

后面是despite+名词做让步状语

他抱病去上班，尽管天气恶劣。
该句子实际上强调了“该死的鬼天气”，尽管如此，他还是went to work with sickness, despite the nasty weather existed. 等于regardless of the disgusting weather.
一个主句，后跟一个条件状语。