High Dimensional Model Representation (HDMR) and its great extension Enhanced Multivariance Product Representation (EMPR) use product type weight functions each factor of which is a univariate function depending on a different independent variable. Either HDMR or EMPR has a very important feature that the constancy measurer approaches 1 from below when the volume of the geometry goes to zero. This urges us to investigate the univariate weight factors at the zero interval limit. This work is devoted to this task. Weight function expansions in powers of the interval length by using regular or single pole expressions as the argument are considered in some details.