My family (myself, wife, three kids) live in a rural area of central California. The USGS recently placed a seismograph on the property adjacent to my own. My property has been in my family for three generations (I inherited it much to the dismay of my other brother, but that's another story).

My wife and I are rather heavy and she is worried we might send a false signal to the seismograph. My question is this: Do we need to tiptoe around the house and yard so as not to disrupt the seismic network?

No, walking or even driving a car around your yard will have no effect on it.