Podkletnov later published a second paper with colleague A.D. Levit, "Gravitational Shielding Properties of Composite Bulk YBa2Cu307-x Below 70C Under Electro-magnetic Field"(Tampere University of Technology Report MSU-95 chem, January 1995). This paper provides even stronger evidence for the weight loss effect. In this 2nd experiment, samples of different composition and weight (10-50grams) were placed at distances of 25mm to 1.5 meters from the rotating disk. The resultant mass losses went as high as around 2% -- undeniably a statistically significant amount.
I think a reason NASA is interested in this is that if such an effect is real, then potentially operating it out of a gravity well (e.g. where we send our space probes) means that it might be useful as a propulsion system. That is, something that can appear to reduce weight (it says mass but in reality the samples were weighed) in a zero gravity field might produce "negative" weight - that is, a propulsion effect. As Einstein pointed out, there is no measurable difference between the exposure to a gravitational field and acceleration (the elevator thought experiment.)