Weak pullups are weak. They won't be good enough against EMI from long wires coming in from distant switches. They are probably good enough for signals local the PCB hosting the microcontroller.
Its nothing to do with resistance, everything to do with stray capacitance, stray inductance, and capacitive or inductive coupling to nearby high speed signals or mains transients. A nearby logic signal can switch at speeds measured in kV/µs, and a few pF of stray capacitance is enough to pick this up.
Good layout will reduce the sensitivity of wiring to pickup (every signal should ideally be in a twisted pair with a ground wire).
Poor layout (ie spaghetti wiring) will easily pickup EMI like this, especially if large area ground loops are present.
Even 3pF has an impedance of a few k ohms at the clock speed of an Arduino Uno, so the stray impedances actually dominate at these frequencies.