You certainly coverted all the bases! Good job.

Instead of bothering to graph all the data and try and make sense of it, Let's start with this:

The 25K20 has a TAD spec of 0.7us min.

At 64MHz, that means all ADCS settings except for FOSC/64 and FRC violate minimum times (Table 19-1).
Using the FOSC/64 setting gives a TAD of 1us

Computing Tc from equation 19-1 for each of the three source resistances gives:
1K = 0.27us
10K = 1.2us
39K = 4.2us

Computing TACQ = Tamp + Tc + Tcoff, given Tamp = 5us and Tcoff = 0 (25degC) produces:
1K = 5.27us
10K = 6.2us
39K = 9.2us

So, since TAD = 1us, TACQ must be a min of ~6-9 TAD for the three different resistances.

Removing all of the measurements that don't fit the above you get:
Code:
*****************************************************
1k resistor in series with input (TACQ=5.27us)
*****************************************************
Input voltage 25.7mV
FRC        6 TAD      Result: 7
FOSC/64    6 TAD      Result: 7
FRC        8 TAD      Result: 7
FOSC/64    8 TAD      Result: 7
FRC        12 TAD     Result: 7
FOSC/64    12 TAD     Result: 7
FRC        16 TAD     Result: 7
FOSC/64    16 TAD     Result: 7
FRC        20 TAD     Result: 7
FOSC/64    20 TAD     Result: 7

Input Voltage: 1.650V
FRC        6 TAD      Result: 511
FOSC/64    6 TAD      Result: 511
FRC        8 TAD      Result: 511
FOSC/64    8 TAD      Result: 511
FRC        12 TAD     Result: 512
FOSC/64    12 TAD     Result: 511
FRC        16 TAD     Result: 511
FOSC/64    16 TAD     Result: 511
FRC        20 TAD     Result: 511
FOSC/64    20 TAD     Result: 511

Input Voltage: 3.286V
FRC        6 TAD      Result: 1020
FOSC/64    6 TAD      Result: 1019
FRC        8 TAD      Result: 1019
FOSC/64    8 TAD      Result: 1019
FRC        12 TAD     Result: 1019
FOSC/64    12 TAD     Result: 1019
FRC        16 TAD     Result: 1019
FOSC/64    16 TAD     Result: 1019
FRC        20 TAD     Result: 1019
FOSC/64    20 TAD     Result: 1019


*****************************************************
10k resistor in series with input  (TACQ=6.2us)
*****************************************************

Input voltage 25.7mV
FRC        6 TAD      Result: 7
FOSC/64    6 TAD      Result: 7
FRC        8 TAD      Result: 7
FOSC/64    8 TAD      Result: 7
FRC        12 TAD     Result: 7
FOSC/64    12 TAD     Result: 7
FRC        16 TAD     Result: 7
FOSC/64    16 TAD     Result: 7
FRC        20 TAD     Result: 7
FOSC/64    20 TAD     Result: 7


Input voltage 1.650V
FRC        6 TAD      Result: 511
FOSC/64    6 TAD      Result: 511
FRC        8 TAD      Result: 511
FOSC/64    8 TAD      Result: 511
FRC        12 TAD     Result: 511
FOSC/64    12 TAD     Result: 511
FRC        16 TAD     Result: 511
FOSC/64    16 TAD     Result: 511
FRC        20 TAD     Result: 511
FOSC/64    20 TAD     Result: 511


Input voltage 3.286V
FRC        6 TAD      Result: 1020
FOSC/64    6 TAD      Result: 1019
FRC        8 TAD      Result: 1019
FOSC/64    8 TAD      Result: 1019
FRC        12 TAD     Result: 1020
FOSC/64    12 TAD     Result: 1019
FRC        16 TAD     Result: 1019
FOSC/64    16 TAD     Result: 1019
FRC        20 TAD     Result: 1020
FOSC/64    20 TAD     Result: 1019


*****************************************************
39k resistor in series with input  (TACQ=9.2us)
*****************************************************

Input voltage: 25.7mV
FRC        6 TAD      Result: 7
FOSC/64    6 TAD      Result: 7
FRC        8 TAD      Result: 7
FOSC/64    8 TAD      Result: 7
FRC        12 TAD     Result: 7
FOSC/64    12 TAD     Result: 7
FRC        16 TAD     Result: 7
FOSC/64    16 TAD     Result: 7
FRC        20 TAD     Result: 7
FOSC/64    20 TAD     Result: 7

Input voltage: 1.650V
FRC        6 TAD      Result: 511
FOSC/64    6 TAD      Result: 511
FRC        8 TAD      Result: 512
FOSC/64    8 TAD      Result: 511
FRC        12 TAD     Result: 511
FOSC/64    12 TAD     Result: 511
FRC        16 TAD     Result: 512
FOSC/64    16 TAD     Result: 511
FRC        20 TAD     Result: 511
FOSC/64    20 TAD     Result: 511

Input voltage: 3.286V
FRC        6 TAD      Result: 1019
FOSC/64    6 TAD      Result: 1019
FRC        8 TAD      Result: 1019
FOSC/64    8 TAD      Result: 1019
FRC        12 TAD     Result: 1019
FOSC/64    12 TAD     Result: 1019
FRC        16 TAD     Result: 1019
FOSC/64    16 TAD     Result: 1019
FRC        20 TAD     Result: 1019
FOSC/64    20 TAD     Result: 1019
Pretty consistent. It shows that waiting longer than the minimum doesn't get you anything, but it also doesn't change anything either.
The interesting thing is as you look through the raw data you can see the effect of not using the proper TAD setting for the clock freq you're using, or not waiting/setting TACQ to at least the minimum time.