If you're generating your derived ground rail using a two-resistor voltage divider (usually with a capacitor from the rail to the negative supply), the values of the resistor are a tradeoff between avoiding wasted supply current (this pushes for higher value resistors, so less current flows through them) and having a "firm" rail, i.e. a rail that stays half way between the positive and negative supply voltages regardless of the state of other signals in the circuit that may be connected to that rail.
In some cases, your derived ground rail is only used to feed inputs of op-amps (typically, non-inverting inputs of op-amps used in inverting configuration), which themselves draw negligible current. In this case, your rail is not going to get "pulled around" by current feeding into or out of it, and you can use 100k resistors with no problems.
In other cases, current will be drawn from, or fed into, the rail by current paths in the circuit. Sometimes a resistor is connected from the derived ground rail to a signal point, to which a signal is coupled. The resistor acts to "bias" the circuit point at a DC voltage equal to the derived ground rail.
But the signal then causes an AC signal to appear across that bias resistor, which causes current to feed through the bias resistor and into the derived ground rail, and this can pull the rail around. Actually, some of the signal is coupled into the rail, and from there, can feed to other parts of the circuit, possibly causing problems.
You can describe the derived ground rail as being "not stiff enough" to hold its voltage steady in the face of varying currents feeding into/out of it. For this reason in AC applications such as audio, it's common to connect a capacitor (typically something like 10 uF) from the derived ground rail to the negative supply rail, which makes the derived ground rail "stiffer" at AC (signal) voltages, while allowing the two resistors to set the DC voltage.
If your derived ground rail needs to be able to supply significant DC and/or AC current while remaining steady, there are other solutions. If you have a spare op-amp in a multi-op-amp package, you can use it as a buffer (with its output looped back to inverting input) to buffer a derived ground voltage created with a pair of resistors as before. The op-amp's output becomes the derived ground rail, and the op-amp supplies all the current, steady and alternating, to everything connected to the ground rail.
The op-amp has a very low output impedance, so the derived ground rail remains very "firm" within a wide range of currents that may be drawn from it at different times. In other words, the derived ground rail remains rock steady at half way between the positive and negative supply voltages regardless of what's connected to it, and what currents those connections may carry, within the limits of the op-amp's output capability.
In unusual cases, you can add a buffer stage of some kind. There's also a very convenient device called the TLE2426 from Texas Instruments, which is a 3-terminal device in a transistor-style package that connects to the positive and negative supplies and generates a regulated and stable derived half-supply-voltage output that behaves very much like the op-amp example.
