You need to provide more detailed information. I found two Willie Parker's and I'm sure there were more.
1920 Justice Precinct 5, Runnels, TX
Willie Parker, b. TN, 50, widow, general farmer
Lennis, son, b. TX, 20, home farmer
1910 Justice Precinct 1, Runnels, Texas
William D. Parker, b. TX, 52, marr 27 yrs, farmer
Willie M., wife, b. TX, 51, had given birth to eight children but only six alive in 1910.
Andrew R., b. TX, 23
Clifford E., b. TX, 15, laborer home farm
Effie L., b. TX, 11
Syble L., b. TX, 9
Ira E. Wood, nephew, b. TX, 23, laborer farm
Also I wouldn't include the W part because her descendants might take offense.
If you have more definitive info about Willie May, I can look her up in Ancestry or FamilySearch. Successful Searching!