Why does Sirius proper motion "wiggle" with a 1 year period, when Sirius A and Bs binary orbit is a 50 year period? Some stars, if observed repeatedly over time, show a perturbation or "wobble" in their proper motion. If this is a periodic occurrence we can infer that the perturbation occurs due to the gravitational influence of an unseen companion. 

In Sirius Matters, Noah Brosch describes a secondary wiggle,

"The trajectory described by the two components of Sirius shows an additional component of motion as tiny wiggles super-posed on the wider modulations of the proper motion by the orbital motion of the Sirius pair. The wiggles have a period of one year. "

What causes this second wiggle?
Your vantage point changes throughout the year as the Earth moves around the solar-system barycentre (close to the centre of the Sun). That means the positions of nearby stars "wiggle" with respect to more distant background stars, with a period of one year; the amplitude of this wiggle is how you determine the parallax distance to the object.

In the case of Sirius AB, this wiggle is superimposed on a motion caused by the binary orbit of the two components in the Sirius AB system and by the motion of the Sirius system with respect to the Sun projected onto the plane of the sky - the proper motion.