A higher maternal BMI was associated with a lower total and moderate physical activity level and a higher sedentary activity level of the child. A higher maternal BMI was also related to a higher BMI and higher waist circumference in the child. A higher paternal BMI was most strongly related to a higher BMI and waist circumference in the child. A higher level of maternal total physical activity was related to higher levels of children’s moderate and vigorous physical activity. Also an inverse relationship between active commuting of the mother with children’s BMI was found. Paternal physical activity was not related to children’s physical activity, BMI or waist circumference.

Genetic predisposition, but maybe more important, the obesogenic environment may be underlying factors for these findings. In young children, parents have a strong influence on their children’s lifestyle. They play an important role in the development of habits related to diet and physical activity [13]. Obesogenic behavior in parents is related to obesogenic behavior of the child [22] which causes a higher risk of development of overweight in these children.

Higher levels of maternal active commuting were related to a lower BMI and higher levels of light physical activity in children. We assume that when a mother goes to her work walking or by bike, she will bring her child walking or biking with her to go to school or daycare. These results suggest that when mothers actively participate with their children in daily physical activity, it may contribute to a healthier BMI of their children.

High parental BMI might be an indicator of an obesogenic environment for the child. Indeed, we found that a higher parental BMI is associated to a higher BMI and waist circumference of the child. These finding are in line with the conclusion from a previous review [23]. A higher maternal BMI was also related to lower levels of total, moderate and vigorous physical activity and to higher levels of sedentary activity of the child. We assume that mothers with a higher BMI may create a more obesogenic environment like being less engaged in physical activities together with the child, or less stimulation of physical activity in the child. This fits with our finding that mothers with a higher BMI were less active themselves. In our study, the relation between parental BMI and physical activity in children is attributed to mothers, but not to fathers. In the Netherlands it is common that both mother and father have a job and combine the care for their child, but still mothers spent the most time in raising their child. Women have more often part time jobs compared to men [24], and children of divorced parents live more often with their mother than with their father [25]. We hypothesize that the maternal contribution to an obesogenic environment is stronger than that of the father in preschool age.

Some previous studies investigated the relation between parental physical activity with preschool children’s physical activity, but only few studies measured physical activity with accurate methods, like accelerometry or validated questionnaires [26–29]. Three of the four studies found a positive relationship between parental physical activity and their preschool children’s physical activity. In these studies, children’s physical activity was measured with an accelerometer [26–28] and parental physical activity was measured with an accelerometer [26, 27] or a validated questionnaire [28]. These studies measured physical activity in children for a longer period than that we did in our study, i.e. 5–9 days instead of 4 days. Two studies measured parental physical activity by accelerometer. This might provide more accurate estimates of total parental physical activity than questionnaires. On the other hand, the questionnaire provides more information on type of activity and on structured activities like active commuting. One of the four studies found no direct relation between parental and children’s physical activity, but the previous reported associations may have been indirect, showing that parental physical activity was positively associated with parental physical activity support, which in turn was positively associated with their children’s physical activity [29]. A difference with our study is that their results were based on a physical activity questionnaire for children about physical activity at home instead of a full day physical activity measurement with an accelerometer. They did measure physical activity with an accelerometer, but only while attending child care. For this measurement they found no relation with parental physical activity at all. One study found that the BMI of the father, but not of the mother predicted children’s preschool children’s physical activity level [30]. We found a relation only in mothers, but not in fathers. A difference with our study is that the previous mentioned study measured physical activity of the children while attending daycare, which may be different from physical activity levels at home. Another study did not find a relation between parental BMI and children’s physical activity [27], but they only included 21 fathers and 72 mothers. More research is needed to draw firm conclusions about this relation in preschool children.

We found no studies investigating the relation between parental physical activity and preschool children’s BMI. Studies in older children (7–12 years) and adolescents (11–18 years) did not show consistent results. More research is needed, especially in preschool children.

Some findings were not in line with our hypothesis. We found that more active children had a higher BMI. Surprisingly, this is also found in some previous studies in preschool children [31, 32]. This finding can be explained in various ways. Our finding could be related to the unreliability of BMI as specific indicator of increased fat mass [33, 34]. In some individuals, BMI may also be higher due to fat free mass, in large part muscle mass. This fits with the finding that the association between total physical activity and BMI seems to be determined mostly by the association between high BMI and more moderate/vigorous activity, as vigorous activities are most anabolic and stimulate fitness level and muscle development. It also seems that the relation between physical activity and BMI or body fat can be dependent on age. A review of Jimenez-Pavon et al. [35] found that the relation between physical activity and adiposity was found more often with increasing age. The inverse relation was found in 60 % (n = 3) of preschool studies; 77 % (n = 17) of studies of primary school-age children, and 86 % (n = 18) of studies of adolescents [35]. This last reason is also in line with our finding that waist circumference was not related to total physical activity. We have no specific reason why higher levels of moderate and vigorous physical activity, and lower levels of light physical activity were significantly related to a higher waist circumference.

A strength of our study is the measurement of physical activity of both parents and children with validated instruments and in children with an objective method, the accelerometer. A drawback is that non-validated cut-off points were used to categorize children’s total physical activity into sedentary, light, moderate and vigorous physical activity. The intensity data results may not be generalizable, because our data were used to generate the cut points. Although it can be safely assumed that the activities classified as vigorous are in the high intensity range, the correct classification of in particular the light and moderate activities is less certain. We would advise the validation of the cut points for future research.