Can my weather station cause interference with my wireless network?
Just because your device operates at 433 MHz doesn't mean that it's the only frequency in use in the device.

I take it you mean 'cheap' as in 'made overseas and not subjected to communication regulatory testing'. Unapproved transmitters may work well, or may not. If it causes interference with other communications, the local communications commission may get upset with you.

An approved transmitter should have this statement (or some equivalent legal boilerplate) somewhere in the manual:

"THIS DEVICE COMPLIES WITH PART 15 OF THE FCC RULES. OPERATION IS SUBJECT TO THE FOLLOWING TWO CONDITIONS:


THIS DEVICE MAY NOT CAUSE HARMFUL INTERFERENCE, AND
THIS DEVICE MUST ACCEPT INTERFERENCE RECEIVED, INCLUDING INTERFERENCE THAT MAY CAUSE UNDESIRED OPERATION."