Well, let’s think through it a bit. As far as I can tell there are three possible explanations, one of which has two possible sources for its explanation.
Explanation 1: It is a hoax. I’m inclined to think that these days it is unlikely that any recent instances of a weeping statute of Mary is a hoax. Examples from further back in the past may very well have been hoaxes to lure unsuspecting pilgrims into the church so that the coffers might fill. But these days I think that is much harder to pull off, what with the technology we have today, and the willingness to prosecute such activities through legal channels. So, depending on when these videos were taken and where they were taken might provided circumstantial evidence one way or another that there was a hoax involved. Just like in videos of Cryptozoology, if there is some grainy home video from 1982, then I would be more suspicious of a hoax. But, if this were more recent and if there were multiple videos of the event by tourists with I-phones, well, then I don’t think a hoax is as likely. The hoaxers, I think, would be taking far too great a risk by exposing not only the trick itself, but also in opening themselves to lawsuits.
Explanation 2: Natural processes. Now, I doubt that this would work if it were actual blood that was recorded on the video, and later confirmed through testing. But, if this was not blood, but something like a red-pigmented oil or paint, then it could just be some natural phenomena. Same with an oily substance dripping from the area around the statue’s eyes. Perhaps some of these statues were even designed in such a way (and this might overlap with the hoax theory) to “sweat” from the area around the eyes in order to have this affect. Maybe it was done intentionally when certain atmospheric conditions obtained, or maybe it happens indirectly when those same conditions obtain.
Explanation 3: Miraculous event. Now, this explanation could have two sources, although, ultimately every explanation could be drawn back causally to God Himself as creator of all things, to include secondary causes and human free will (a free will that could choose to instantiate a hoax upon unsuspecting pilgrims). But, let’s say this is an instance of an actual supernatural miracle. In other words, especially if it were demonstrated that it was real blood coming from the statue’s eyes, these kinds of phenomena would not obtain in this spacetime reality based solely through the natural causal powers acting upon the properties of the statue within the environmental context the statue is in. Some other causal source for the phenomena is required
The first supernatural source that it could be would be God’s own causal powers to enact such an event. In other words God efficiently caused the statue to weep blood. This is certainly possible, and if God wanted to use this weeping statue to draw people into some knowledge of His divine presence, then I could easily imagine Him doing that. So, source one of a supernatural occurrence like this could be God’s causal powers.
The second source would be that of a demonic agent. Demons may be able to affect the physical world, in fact I think the Bible makes it abundantly clear that Demons can interact with the physical in some way (Job 1-2, 1 Thess 2:18, Mk 5:11-13, Lk 9:38-42, Lk 13:11-16), although some have argued that demons can only interact with the non-physical (e.g. with the human soul or mind). Still, I think there is scriptural evidence and evidence from exorcism and deliverance ministries that demons can interact with material object. If that is the case, then this could be an example of a demon altering the subatomic particles or physical properties of the statue so as to make it weep oil, or blood, or whatever. The reason for this would likely be to try and trick viewers in some way, perhaps make them think, for example, that the power of God is in things like statues, or that Mary is somehow worthy of worship, or whatever. That said, I think even if there were instances of phenomena like this that were caused by a demonic will, God could still use the same phenomena to affect the right kind of change in the human viewers. So, some viewers might see the weeping blood as a sign of God’s power working in the world and rightly give Him glory, but others might see it as a sign that they should worship Mary as if she was divine, or some such thing.
Hope that helps. Interesting question to be sure.