[Sir Kohran]

I think that's because it's the first time Grima realises just how terrible Isengard has become. When Saruman first made the offer of drugging the King to him, I don't think he really thought about what the consequences of helping Saruman would be - he just wanted Eowyn, and blinded himself to the reality of what he was doing. But with Rohan weakened, Isengard built up its army, which, as we all know, was there to kill everyone in the Hornburg - including Eowyn and all the others Grima had ever known or cared for - and he's had a big hand in it. Grima realises this when he sees Saruman (who only insults or ignores him by that point) and this terrible army of Uruk Hai, but too late by then, and I think he knows that when he cries.

It's all a build-up to when he turns on Saruman at the start of ROTK (EE), when Theoden offers him a second chance, and he realises he's been on the wrong side all along. But by then,it's once again too late, and he dies a tragic, almost Shakespearean death, only killing Saruman when he might have been of some use to the Free Peoples, resulting in his death at Legolas's arrows.