This study clarifies the absorption behavior of micro-droplets of water on treated paper to support the design of functional microstructures, such as electronics and micro-fluid channels, on paper. The period of time between when a micro-droplet of water ejected from an ink-jet head lands on the paper's surface and its complete disappearance by absorption was defined as the micro-sizing degree (MSD), and an MSD measurement method was established. The MSD was evaluated using microscopic high-speed video images of the side view recorded every millisecond. Several grades of commercially available ink-jet paper media and laboratory sheets having different levels of water repellency prepared from a pulp and a sizing agent were examined. The MSD of commercial ink-jet papers, which are known to absorb water very quickly, was 3-6 ms. Weakly sized laboratory sheets exhibited a lower MSD of 2-3 ms. The absorption behavior was analyzed in terms of the capillary pressure with and without the Laplace pressure; the theoretical and experimental results agreed moderately well. The results indicated that the Laplace pressure cannot be neglected in the analysis. The MSD of a wet surface where a preceding micro-droplet had already landed was higher than that on a dry or partially wet surface, presumably because water remains inside pores for an unexpectedly long time.