Death by a thousand bruises Weyland. Except for the little problem that meat damage tends to come in big packages, not small, and you only get 1 counter regardless of amount of damage.
It's nice for fast advancement if you have Crisis Management or Dedicated Response Team and can keep the runner tagged. But eh, a runner staying tagged against Weyland is not likely to survive anyway.
Probably your best bet to make Reconstruction Contract work is to combine it with the thematically appropriate Weyland Consortium: Builder of Nations. In the best case that gives you a free counter every turn, provided the runner doesn't trash your contract.
I'm not saying Reconstruction Contract can't work. But it seems like a card that you'd toss into a BoN deck thinking "it's cheap and potentially I'll score an agenda with it".
One thing that is useful about Reconstruction Contract is that it can provide a way to add one or two missing advancement tokens to an agenda relatively easily and safely. At 4 to trash the runner is less likely to go after it so as long as it's not an obvious Government Takeover scoring option it should be relatively safe. Meanwhile scoring out a Corporate Sales Team in one turn is quite useful.