Weekly data from 7 years (2004–2010) of primary-care counts of acute respiratory illnesses (ARIs) and local weather readings were used to adjust a multivariate time-series vector error correction model with covariates (VECMX). Weather variables were included through a partial least squares index that consisted of weekly minimum temperature (coefficient = − 0·26), weekly median of relative humidity (coefficient = 0·22) and weekly accumulated rainfall (coefficient = 0·5). The VECMX long-term test reported significance for trend (0·01, P = 0·00) and weather index (1·69, P = 0·00). Short-term relationship was influenced by seasonality. The model accounted for 76% of the variability in the series (adj. R
2 = 0·76), and the co-integration diagnostics confirmed its appropriateness. The procedure is easily reproducible by researchers in all climates, can be used to identify relevant weather fluctuations affecting the incidence of ARIs, and could help clarify the influence of contact rates on the spread of these diseases.