Martha is almost certainly related to John ROBARDS, the 1710 immigrant from Wales to Virginia, whose widowed daughter-in-law — among other ROBARDS — settled in Jessamine Co., KY, in the late 1700s, but I have not as yet been able to make the connection.  ROBARDS is a rare surname, and I've little doubt all the ones in Jessamine Co., KY, in the late 1700s and early 1800s were related, but many of these have yet to be "connected." 

1a.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):  not found.

1b.  Jordan R. Dodd, ed.  1993.  Indiana Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-228):  no remarriage of Martha/Patsy WILLIS found, but the Sullivan County Courthouse was burned in 1853, so no marriage records

2.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  not found.  The newlyweds are probably living with his parents or hers.

3.  1830 Census Index and Digital Images (online at Ancestry.com; Image #51-52 of 56; extracted by Diana Gale Matthiesen):

1830

IN

Sullivan Co.

pp. 192B/193A

Levi Willis

210 010 - 011 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1825-1830	= Son B = Son A
1 male	5-9	1820-1825	= John (b. 1824)
1 male	20-29	1800-1810	= Levi
1 female	5-9	1820-1825	= Daughter B
1 female	10-14	1815-1820	= Daughter A
1 female	20-29	1800-1810	= Martha

4.  Family Quest Archives:  Indiana 1840 Census: St. Joseph, Stark, Sullivan, & Steuben Counties.  Heritage Quest CD M704-94 (extracted by Diana Gale Matthiesen):

1840

Willis, Martha

IN

Sullivan Co.

p. 50

022 000 - 010 101

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	5-9	1830-1835	= Son D = Son E
2 males	10-14	1825-1830	= Son B = Son A
1 female	5-9	1830-1835	= Daughter C
1 female	15-19	1820-1825	= Daughter B
1 female	30-39	1800-1810	= Martha

John was age 15 or 16 in 1840, so we really would expect to find him in the home, though his absence could simply be enumerator error.  On the other hand, a widow with seven children in the 1840s could be in dire straits, so it would not be surprising to find John, her eldes son, living and working outside the home.

5.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  Martha not found.  John is married and living in Haddon Twp., Sullivan Co., IN.

6.  Messages in the Willis Family Genealogy Forum (online at GenForum.com).