How are Microchip configuration straps used?
The weak pull-up/pull-down being referred to is internal to the device. Typically they are 50k-100k; actual value depends on the design and due to the manufacturing process may vary quite a bit.  As stated, the weak pull-up/pull-down is simply there to prevent the pin from floating if it is not connected to anything.
To set a configuration, one needs to connect a stronger pull-up/pull-down resistor externally. Typically 10k is used. This value will over power the internal pull-up/pull-down but is not too strong to interfere with the output when driven.
When the device is in reset, the output pads are disabled and in a high impedance state. At this point the pull-up/pull-down resistors pull the pin high/low as desired. As soon as reset is released (see the data sheet timing) the device will capture the state of these pins and configure itself for the proper operation. At this time the device will then enable the output driver.