The acute increase in Resting Metabolic Rate (RMR) observed in response to strength training persists for between 24 and 38 hours, indicating that we would need to train from between 4.5 (or 9 times per fortnight) and 7 days per week in order to maintain this elevated level!
The 7% increase observed in this study—9% for men and 4% for women—was not, of course, the consequence of an increase in muscle mass, but is believed to be associated with hormonal changes relating with repair and recovery. And although the value is not insignificant, it equates to just 660 kJ (~155 Cal) per day for men, and 220 kJ (~55 Cal) for women. For men, that is roughly equivalent to a half-hour walk. The training workload, itself, would contribute more to the subjects' daily energy expenditure.
More persistent gains can be made with ongoing strength training producing an increase in fat-free mass (FFM)—muscle. One study observed an average ~5% increase in RMR after a 9-month resistance training regimen, which could be explained partially by the consequent increase in muscle. Such permanent changes are commonly promoted as the benefit of strength training over aerobic endurance training. But unfortunately, these are also limited: skeletal muscle contributes just 54 kJ (13 Cal) per kilogram per day (kJ/kg/d) to our RMR, compared with 440 kJ/kg/d for cardiac and kidney tissue, 240 kJ/kg/d for the brain, and 200 kJ/kg/d for the liver. Given that the average (median) height-adjusted Fat-Free Mass Index (AdjFFMI) of untrained men and women is 18.9 and 15.4 kilogram metres (kg.m), respectively, and given also that the AdjFFMI for the average (male) college-level athlete was found to be 22.8 kg.m, we can fairly assume that most people—anticipating that they will not train to professional level—will be limited to about 14 kgs (30 lbs) of muscle gain, with a great deal of genetically-determined variance either way, of course. This upper limit equates to 665 kJ (182 Cal) per day, and considerably less for women. Thus, strength training has the potential to increase our RMR by ~800-1,300 kJ (~200-300 Cal) per day, accounting for both increases in FFM and hormonal changes from regular training—an energy expenditure that would be matched or exceeded by an hour-per-day strength training commitment.
There is no doubt that strength training and muscle mass have a positive influence on our RMR, but the common belief that it is comparable to aerobic endurance training is supported neither by theory nor empirical observation. The literature consistently reports that aerobic endurance training results in (many times) greater fat loss than strength training, with strength training contributing either very little to fat loss, or an amount that is statistically insignificant.
In contrast to strength training, aerobic endurance training is continuous, yielding far greater energy consumption per unit time. And although it does not result in the increases in RMR that are observed with strength training, it is subject to Excess Post-exercise Oxygen Consumption (EPOC), which has both short-term (< 2 hours) and long-term (up to 48 hours) effects, which are a function of exercise intensity. In terms of its potential, even a moderate Functional Threshold Power (FTP) of 200 Watts, for example, would result in an energy expenditure of 3,600 kJ (860 Cal) for an hour's effort, plus perhaps as much as 10% more for EPOC. Moreover, aerobic endurance can be trained every day without the need for physical recovery. Tour de France riders consume, on average, 25,000 kJ (~6,000 Cal) for every day of competition, with the maximum of around 36,000 kJ per day for the outliers. These sorts of figures are simply not possible to achieve with strength training.
So in conclusion, strength training once per week (or even three times) will unfortunately have a negligible effect on fat loss. The evidence clearly demonstrates that aerobic endurance training is many times more effective in reducing body fat.