1830 census of Lee Co., Virginia, lists on p. 21, line 25:
Eldredge, Jesse, 1 male 20-29, 1 female 15-19, 2 females under 5.

The preceding household is headed by a James Eldridge in his 60’s, probably Jesse’s father. (It is a page of all E surnames, so unlike most censuses, this one is not recorded in location order. The names are not alphabetized beyond initial, though, so while there is no evidence that James and Jesse were living next door, they were the closest E names to each other.)

1840 census of Morgan Co., Ky, lists on p. 27, line 29:
Jesse Eldridge: 1 male 30-39, 1 female 20-29; 1 female 10-14, 1 male 5-9, 2 females 5-9, 1 male under 5, 2 females under 5.

Neighbors are William Pew and Joseph Pew (usually spelled Pugh). Above on line 18 is the family of James Eldridge in his 20’s.

1850 census of Morgan Co., Ky, enumerated 29 Aug, lists on p. 75 as family #481:
Jesse Eldridge, 44, farmer, b. Va; Mary, 30, b. Va; Lear (fem), 12; James, 11; Rachel, 8; Susan, 6; Mary, 5; Nancy, 2. All children born in Kentucky.

They are surrounded by Cotton families: Jobe and John before them, and James after.

1860 census of Morgan Co., Ky, district 1, West Liberty P.O., enumerated 12 July, lists on p. 54 as family #328/325:
Jesse Eldridge, 54, farmer; Mary, 48; Susan, 16; Nancy J., 12; Rebeca, 10; Ruth, 8; Jesse, 6. Elihu Brinley, 5; Jesse, 3. All born in Kentucky.

Two households below is a family headed by Joshua Eldridge age 45 with wife Fanny age 40.