I don't think plugging a tire weakens it much at all. The steel cords are extremely tough, and there are more than one of them. It more like a lattice work of cords. Even if it were possible to cut thru one single steel cord, the tire wouldn't just suddenly disintegrate. Now if we were talking about a gash, or a hole in the sidewall, that would be very different, in that case, replace the tire. But a small hole in the rubber, in the middle of the tread, that doesn't threaten the strutural integrity of the tire much, in my country-boy estimation.
One thing to think about, is that as the tire tread wears, the plug wears with it, and eventually the plug gets very short, and might come out, or be disturbed by road forces and high temperatures. This may result in rapid air loss, that might surprise you. Thats probably why Michellin recommends mushroom shaped plugs that have some grip on the tire from the inside.