It's weeks since I was ill.It's weeks since I fell ill.

e 动词是延续性动词,是系动词,表示状态,该状态可以延续.be ill 生病的状态.
It's weeks since I was ill.我病好了好几个星期.（从生病状态结束,也就是从身体康复,到现在有几个星期了.）
fall 是结束性动词（终止性动词）,该动作发生后很快结束.fall ill 生病的动作,由没病变为有病这个短暂的动作.
It's weeks since I fell ill.我生病已好几个星期了.（从开始发病到现在有好几个星期了.)