It isn't a Colpitts oscillator, it's a Hartley oscillator. The two are very similar but Colpitts uses a center-tapped tuning capapcitor and a Hartley uses a center-tapped inductor.
The tuned circuit in your design uses an inductor with a center tap at which the DC power to the transistor is connected. The choke is to filter noise from the supply line to stop it modulating the frequency and the capacitor to ground is to ensure the center tap is 'ground' as far as signal are concerned.
The tuning capacitor across the inductor is made in two parts. The first part is the single fixed capacitor C9, the second is the varicap in series with a fixed capacitor C7. To the tuned circuit it looks like one capacitor although in reality it is three, two fixed and one being the varicap.
One side of the varicap is always at supply voltage by virtue of being connected through the tuning inductor and choke, the other side is held a lower voltage by the bias resistors on the amplifier stage. The varicap is always reversed biased, in other words always behaving like a capacitor and never conducting DC. The amount by which it is reverse biased depends on the DC and on the modulation signal, together they set the center frequency and provide frequency modulation. Because there is oscillation voltage on the varicap, R6 is necessary to prevent the output of the amplifier absorbing some or all of it which might stop the oscillator running altogether. Because no DC current is flowing through it (varicap isn't conducting) the value is relatively unimportant. The value chosen is a compromise between loading the oscillation if it's too low and the high frequencies in the modulation being attenuated if it's too high.
Brian.