Perhaps I am wrong, but my interpretation of the records are as follows:

1850 census District 38, Hall, GA

Matthew Hawkins, 35, born 1815 SC
B Hawkins 6 (Balaam, son of Matthew)
J Hawkins 4 (Joseph, son of Matthew)
M Hawkins 4 (Malinda, daughter of Matthew)
Benjamin Hawkins 43 (brother of Matthew)
R Hawkins 37 (Rebecca probable wife of Benjamin Hawkins)

I have Benjamin died in 1853, not sure where I got that info.

1860 census District 403 Hall, GA

M Hawkins, 44 (Matthew)
Balaam Hawkins 14
Joseph Hawkins 13
Malinda Hawkins 13
R Hawkins 46 (Rebecca, widow of Benjamin, Matthew's SIL)
Tyra Hawkins 10

I have Tyre Hawkins as the only son of Benjamin Hawkins and wife, Rebecca.

Does this make sense or am I totally off base??