Actually, I would argue that Chinese success in weightlifting is one of those caused by heavy government funding. The Chinese model of weightlifting development (starting talent super youge, putting them through special development schools, and picking out the best, and then training them even more / giving them state funding) is exactly the type of money heavy technique that India appears to not have.

Yes, but it's not the only model for success.

The point is that national tallies can be thrown out by the internal medal-granting dynamics of sports.

If weightlifting still gave individual medals for the snatch and the clean & jerk as well as the total, it'd be even more noticeable.