According to most observers, arms shipments from Iran to Hizbollah normally move by air. The shipments were frequent enough to be fairly routine. The equipment was placed aboard Syrian aircraft, thus giving both Iran and Syria some deniability, since they can claim the equipment is for Syrian use. Flights usually end at Syrian military airfields, from which the equipment is then transshipped overland to Lebanon. While the withdrawal of Syrian troops from Lebanese frontier regions over the past year made the movement of equipment overland more difficult, it certainly didn't halt it. Apparently, within days of the onset of the Israeli offensive, Iran ceased shipments of equipment, in some cases actually unloading aircraft that were ready to take off.
The Iranian reaction seems to have several roots. Naturally, there's considerable irritation over Hizbollah provoking a major crisis without consulting Iran. Despite President Mahmoud Ahmadinejad's frequent fiery rhetoric, he seems disinclined to have a confrontation with the US (as any serious resupply of Hizbollah would like bring on), at least for the present. Moreover, the real authority in the country remains in the hands of the Islamic clergy. Supreme Leader Ayatollah Ali Khamenei is considerably less radical than the president, who chaffs under his authority. Khamenei may also have a better understanding of the feelings of the bulk of Iran's middle class. The country's burgeoning middle class resents the enormous subsidies that have gone to Hizbollah (by some accounts as much as $250 million a year), when the country's economy is still shaky, poverty is widespread, and opportunity for a better life seems elusive. These are issues that are probably also beginning to irk the rural peasantry, who, very conservative in religion, form the backbone of Ahmadinejad's political support.
At least one spokesman for Hizbollah has publicly admitted that the organization did not expect Israel to react so strongly to the raid two weeks ago that touched off the current round of fighting. Hizbollah seems to have thought of the raid as PR stunt, to which Israel might reply with a couple of artillery shells or a kidnapping attempt against Hizbollah leaders. Because of this, they did not clear the operation with their sponsors in Iran. The sudden eruption of a full scale crisis for which many, in the West as well as in the Middle East, are holding them responsible, caught the Iranians off guard. It also seems to have annoyed them. As a result, despite considerable rhetoric emanating from Iranian leaders promising support for Hizbollah and death for Israel, Iran appear to have shut down shipments of equipment.