Or if you want the math treatment (since i'll feeling patient
VOltage across the two resistances = 5V = Voltage drop across Resistance 1 (V1) + Voltage drop across Resistance 2 (V2). V2 is the voltage you'll see on Arduino pin.
Ohm's Law: Voltage (V) = Current (I) * Resistance (R)
Resistance R1 = 10kOhm, Resistance R2 = your weather gizmo.
However, current flowing through the wire from 5V to Ground (neglecting the very very minor amount that will flow through Arduino pin) is the same, ie = I
Therefore, V = V1 + V2 = I*R1 + I*R2 = I*(R1+R2)
ie. "equivalent resistance" of 2 resistors connected in series = R1 + R2
or re-arranging, I = V/(R1 + R2)
Therefore the voltage you'll see at Arduino Pin = V2 = I * R2 = V/(R1 + R2) * R2 = V*R2/(R1 + R2)
And so you see how the voltage you see on Arduino pin is affected by R2