How much does it cost extra to fly with one additional passenger?
I am basing the following calculations on the excellent answer by Peter Kämpf to this question: How much of an improvement would a 1% weight decrease on an airplane be to the industry?.

We can approximate the fuel usage with the Breguet equation

$$ m_\mathrm{TO} = m_\mathrm{Landing} \cdot \exp \left( \frac{R \cdot g \cdot b_f}{v \cdot L/D} \right) , $$
where:


$m_\mathrm{TO}$ is the total mass at takeoff
$m_\mathrm{Landing}$ is the total mass at landing
$R$ is the distance flown
$b_f = 0.000018 \mathrm{kg} / \mathrm{Ns}$ is the fuel burn
$v=250 \mathrm{m}/\mathrm{s}$ (about 900 km/h) is the velocity
$L/D=18$ is the lift to drag ratio


Assuming a fully loaded A320 (OEW $ = 42.6 \, \mathrm{t}$ with $ 19.9 \, \mathrm{t}$ payload and $3 \, \mathrm{t}$ reserve fuel $\Rightarrow m_\mathrm{Landing} = 65.5 \, \mathrm{t}$), we can do the calculation for the fuel ($m_\mathrm{TO} - m_\mathrm{Landing}$) with and without an extra 100 kg and compare for different distances $R$:


Note: this equation become increasingly inaccurate towards small distances because the takeoff, which uses more fuel, is not taken into account here.

Using the given speed, this can be converted to different flight times:


And by multiplying with the current jet fuel price of 616 US Dollars per metric ton, we get the additional cost of a 100 kg passenger per flight time: