SF6 is 23,000 times more potent, weight for weight, than CO2, whereas CF4 endures in the atmosphere for about 50,000 years.
SF6 is primarily used in the electrical industry, while CF4 is related to electronics and aluminium manufacture.
Yet according to the Intergovernmental Panel on Climate Change (IPCC), these industrial gases contribute only about 1% of the man-made greenhouse effect.
Professor Weiss's research - and that from other groups - suggests their contribution may have been underestimated.
In almost every case, atmospheric concentrations are higher than suggested from emissions data, which suggests there is a pattern of under-reporting, he said.
Most of the instruments monitoring the air are based in isolated regions in order that measurements accurately reflect the global background level rather than local sources.
But regional monitoring is starting to locate problem areas, Professor Weiss related.
"There are [scientific] papers submitted for publication measuring HFC23, a byproduct of making a number of other gases including refrigerants," he said.
"People have modified their factories to burn the gases rather than release them; we're making measurements of HFC23 in Asian areas and we're seeing results that are inconsistent with people burning as much as they say they're burning."
Money for that burning is channelled through the Kyoto Protocol's Clean Development Mechanism (CDM).
This is intended to provide western companies with a cheap way of reducing emissions by paying for it to happen in the developing world.
This should result in money being channelled into poorer countries, assisting their development.
However, most of the money so far has gone to China, where companies have the resources to make the most of the system.
Lex de Jonge, chairman of the CDM's Executive Board, told BBC News he "had no doubt" that CDM projects were creating the reductions they were designed to.
"I can assure you that the reductions under the CDM are real, because they are checked and cross-checked and monitored," he said.
"But another issue is whether there are other sources of HFC23 that are putting this material into the atmosphere."
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