The particular aircraft A.M.M. Chapter 5 (Conditional Inspections) will spell out what constitutes a hard landing and an overweight landing and the inspections that are required. You're usually sent to pull the DFDR readouts by the crew reporting a hard or overweight landing. For those aircraft that lack sophisticated DFDR's the crew's report is about all you have to go on and that's always worked for me.
For example the B777-200 AMM says:
"An indication of a hard landing on the main landing gear is a peak recorded vertical
acceleration that exceeds 1.9 G (incremental 0.9 G). This vertical accelerometer data must be measured by the flight data recorder accelerometer at a data sampling rate of at least eight (8) samples per second. This vertical acceleration G-level threshold is valid for a conventional landing with impact with no more than two (2) degrees of airplane roll, main landing gear touchdown first and normal rotation onto the nose gear".
And for an overweight landing, the same manual says;
"When the airplane lands at a weight that is above the maximum-design-landing weight (MLW), it is an overweight landing".
There are no caveats for accumuluation or deferrals of inspections in the B777 manual and I can't say I've ever seen one, but then I don't know everything; as far as I know one hard landing equals one hard landing inspection, with the same constraint for overweight landings.