Why did Grima shed a tear?

In the book it was explained that Grima's final plan in Rohan (or at least what Saruman had promised him) was to marry Éowyn and become the next King of Rohan (of course still at the orders of Saruman). Not only did he want the throne but he also wanted Éowyn herself.

Saruman had just ordered his army to go to Helm's Deep and kill everyone there, which would have included Éowyn. This is when Grima, counting on Saruman's army victory, shed a tear (for Éowyn).

While I think @SJuan76's answer is on the right track, it's too specific. There is no indication he sheds a tear for Eowyn specifically, as he can't even be sure she's at Helm's Deep. I think many events indicate he's shedding a tear for the end of Rohan. There are multiple indications in the movie he's deep down still a proud man of Rohan.

• After Isengard's fall he seems willing to accept Theoden's offer of redemption.
• He eventually kills Saruman after the latter deeply insulted Rohan.
• In a conversation with Eomer it is shown he wanted Eowyn as price for his betrayal. This indicates he both did not think Rohan to fall and he wanted a strong tie to the remaining country, choosing a wife of Royal descent, probably even ruling it as a Vazal of Saruman (though I admit this is a bit of conjecture).
• Up until the events of the movie he was working a long con, essentially crippling the Rohan Military and head of state, but not (to his knowledge) bringing the destruction of Rohan.
• The tear comes directly after Saruman stating "There will be no dawn for Men", or more specifically the Rohirrim.

This all strongly seems to suggest it is only at that moment he understands that Saruman will settle for nothing but the complete destruction of Rohan and he sheds a tear for his betrayed, but still beloved country.

Grima has just been arguing with Saruman about how strong Helm's Deep is and how it is virtually un-breachable. My interpretation is that he has always seen Helm's Deep as the ultimate in protection and power, and in this moment he is shown power that he's never known to be possible. He was unaware of the power of the black powder and he claims that there is no such army that can breach the walls only seconds later to be shown such an army in the Uruk Hai. He is overwhelmed by it all and sheds a tear at the "beauty" and "fear" of it all. He's shown the evidence of what he only seconds ago doubted was possible and this is his full "conversion" moment.

Below is the movie script taken from IMSDb.com and provides some of the insight and context I'm referring to.

Grima (V.O.): Helm’s Deep has one weakness. Its outer wall is solid rock but for a small culvert at its base which is little more than a drain.

[Camera turns to Gríma and Saruman at Orthanc. Saruman is pouring some dark dry substances into a vessel. Gríma is holding a lit candle in his hand.]

Grima: How? How can fire undo stone? What kind of device could bring down the wall?

[As he steps closer to the vessel, Saruman takes hold of Gríma’s hand and pushes the candle away from the vessel firmly.]

Saruman: If the wall is breached, Helm's Deep will fall.

[He walks away towards the balcony.]

Grima: [Following Saruman] Even if it is breached, it would take a number beyond reckoning, thousands to storm the keep.

Saruman: Tens of thousands.

Grima: But, my lord, there is no such force.

[Both of them came onto the balcony of the tower. Gríma suddenly sees and hears the enormous armies laid out below in neat rows and is astounded and awed. He continues to hold the extinguished candle aloft as he gapes at the vast army below. A horn is sounded, announcing the appearance of Saruman. A loud cheer is heard from the army. Saruman raises a hand.]

Saruman: A new power is rising. Its victory is at hand!

[The army cheers and roars.]

Saruman: This night, the land will be stained with the blood of Rohan! March to Helms Deep! Leave none alive!

[The camera keeps zooming out from the balcony over the incredible size of Saruman’s army, past Uruk-hai, spears, and banners and yet more Uruk-hai. The camera focuses back on Saruman who then raises his hands in the air]

Saruman: To war!!

[The army cheers and roars even louder.]

Saruman: [Sneers] There will be no dawn for Men.

[A tear flows down Gríma’s cheek. The Uruk-hai army began their march to Helm’s Deep.]

This question has a word of god answer on the SciFi sister site. Turns out, both theories are right, to some extent; that is: the tear is both from awe at the military might, and regret at the imminent destruction of mankind. Citing both the actor who played Gríma and the director (via the director’s commentary on the DVD of The Two Towers) the answer notes that the scene makes explicit reference to Nazi propaganda and military shows of force, which had the purpose of creating feelings of awe.

But the answer also cites the writer who notes Gríma’s regret at what he has unleashed. Here’s the relevant excerpt:

Brad Dourif (Gríma Wormtongue): There is no other character who could have brought over to the audience what was about to happen, who could have sold the awe. […] When you look at a picture of something, it isn’t the picture that sells it, you know. I mean the fact that he did an allusion to [the Nazi propaganda movie] “Triumph of the Will”, but that in of itself is not enough, but when you have the person that made it happen suddenly, absolutely come to grips with what it is that he has done, then it’s scary. […]

Peter Jackson (director): This is Nuremburg really. That is the obvious influence for all this stuff. That sort of imagery is so potent and it is useful to dip into those historical references just to press buttons in people.

Philippa Boyens (screenplay): I loved that performance from Brad Dourif just showing that Wormtongue was a man once — what has he done — what has he unleashed?

It’s worth noting that there is no indication that the tear was shed specifically for Éowyn.