We report results of 6.7GHz methanol maser monitoring of 139 star-forming sites with the Torun 32-m radio telescope from 2009 June to 2013 February. The targets were observed at least once a month, with higher cadences of two to four measurements per week for circumpolar objects. Nearly 80 per cent of the sources display variability greater than 10 per cent on a time-scale between a week and a few years, but about three quarters of the sample have only one to three spectral features that vary significantly. Irregular intensity fluctuation is the dominant type of variability and only nine objects show evidence for cyclic variations with periods of 120 to 416d. Synchronized and anticorrelated variations of maser features are detected in four sources with a disc-like morphology. Rapid and high-amplitude bursts of individual features are seen on three to five occasions in five sources. Long (>50d to 20 months) lasting bursts are observed mostly for individual or groups of features in 19 sources and only one source experienced a remarkable global flare. A few flaring features display a strong anticorrelation between intensity and line-width that is expected for unsaturated amplification. There is a weak anticorrelation between the maser feature luminosity and variability measure, i.e. maser features with low luminosity tend to be more variable than those with high luminosity. The analysis of the spectral energy distribution and continuum radio emission reveals that the variability of the maser features increases when the bolometric luminosity and Lyman flux of the exciting object decreases. Our results support the concept of a major role for infrared pumping photons in triggering outburst activity of maser emission.