Do not assume that Iranian policy has to be any more straightforward than that of any other country.
Remember, at the time of the Iran-Iraq War and the Iran-Contra affair, we were playing both sides against the middle with the encouragement of our Israeli allies who were at the same time "running" Pollard against us and who they now want us to release because it wasn’t a serious matter that he was pilfering documents on the USSR out of Navy files for them to copy for whatever reason.
Life is not simple. In the Middle East they are more honest than most of the rest of us. They believe that all serious diplomatic and government policy business has to be hidden and takes place "under the table." (tahta tawila) It is usually the case that Middle Eastern countries assume that embassies are for ceremonial and consular purposes. Therefore if they have something serious to say, they send "secret" envoys to discuss the matter in the best tradition of mediation. (wasta) These envoys can be either oficials or, better yet, persons of influence (ayyan) who are thought of at home with great respect for their important role in affairs of state. Everyone in the region wants to be such a "secret envoy," presumably because it is the key to being in the "inner circle," "in the loop," and maybe someday powerful and rich. The plethora of "secret envoys," real and pretended (hopeful), is sometimes quite comic. Ratio of "Real" to "Pretended" is probably something like 1:3.
Against this background the possibility that the Iranian government might at one and the same time be doing all of the following things simultaneously is quite plausible.
1-Everything in their power to make sure that a Shia dominated government emerges in Iraq to expand the circle of their influence and co-sectarians.
2-Providing weapons, money, training and a virtual army of advisors against the day when Shia action and Iranian "volunteers" might be needed to make sure that the authority of that friendly government "sticks."
3-Running weapons and new IED technologies to the Sunni insurgents to make them potent enough to keep us headed for the door eventually.
Hey! Why Not!
If the Sunni insurgents get us out of the country after bleeding all over the place, then the Iranian logic may well be that a combination of Iraqi troops and Iranian "friends" will be in a good position to deal with them while the USG looks on benevolently from a distance at its protege government and a politically varied spectrum of fatheads say, "Well, that’s democracy…"
Hizballah? What? Hizballah is a specifically Lebanese creature of the Islamic Republic of Iran as represented by the "boys" of the Iranian Revolutionary Guards Corps assigned to the Ministry of Intelligence. Paraphrasing – "They don’t need no stinking Hizballah."