This information has not yet been revealed by Niantic, so the majority of information on this topic was compiled by regular Pokémon GO players.
Why does Size (Weight) matter?
When I take part in Gym battles, I can easily notice a different attacking Speed between some of my Pokémon. For instance, my Exeggutor is XL in Size, and uses its Primary attack extremely slowly. This does not apply with my Scyther and my Jolteon, though. These Pokémon are extra small in size and attack at a very highly rate. Most evidence supports the fact that size influences your attack speed in combat. Even my friends have the same results as I.
Why does Height matter in Pokémon GO?
Height was discovered by many tests in line to determine HP. A Reddit user who was experimenting with this question used this example:
Zubat #1: 3KG (Extra Small); Height 1.80m; HP 30
Zubat #2 4KG; Height 1.60; HP 25
This exampl shows that the weight has no correlation to the Health, but the Heighy does indeed. I checked this with my Psyducks of the CP and still found this principle to be true.
Source: https://m.reddit.com/r/pokemongo/comments/4skhzw/pokémon_weight_and_height_explained/ as well as some side research.