1.  Marriage Record:

2.  1810 Census Index and Digital Images (online at Ancestry.com):  can't find.

3.  1820 Census Index and Digital Images (online at Ancestry.com; Image #2 of 6; extracted by Diana Gale Matthiesen):

1820

PA

Huntingdon Co.

Henderson Twp.

p. 67

Mathew Hall

010001-02110-0-100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-15	1804-1810	= John (b. 1805/6)
1 male	45 or over	in or bef. 1775	= Matthew
2 females	10-15	1804-1810	= Daughter C = Daughter B
1 female	16-25	1794-1804	= Daughter A
1 female	26-44	1775-1794	= Delilah (b. 1785/6)
1	person engaged in agriculture

Matthew is in the wrong age-class, yet surely these are our subjects.

4.  1830 Census Index and Digital Images (online at Ancestry.com; Image #85 of 86; extracted by Diana Gale Matthiesen):

1830

PA

Huntingdon Co.

Henderson Twp.

p. 137

Mathias Hale

111 010 010 - 000 000 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1825-1830	= Matthew Jr. (b. 1828/9)
1 male	5-9	1820-1825	= ?
1 male	10-14	1815-1820	= ?
1 male	20-29	1800-1810	= John (b. 1805/6)
1 male	50-59	1770-1780	= Matthew
1 female	40-49	1780-1790	= Delilah (b. 1785/6)

It's a stretch to make this household our subjects — where did the girls go? and where did the boys come from? — but "Mathias Hale" is the closest I could come to Matthew Hale — and I checked every page of Henderson Twp., line-by-line.   Note that there is no Mathias Hale in Huntingdon Co. in 1820 or 1840.  Listed two lines from Shadrach CORBIN, who is next to Micajah CORBIN.

5.  1840 Census Index and Digital Images (online at Ancestry.com; Image #3 of 20; extracted by Diana Gale Matthiesen):

1840

PA

Huntingdon Co.

Henderson Twp.

pp. 202B-203A

Matthew Hall

001 000 001 - 000 000 010

0000000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-14	1825-1830	= Matthew Jr. (b. 1828/9)
1 male	60-69	1770-1780	= Matthew
1 female	50-59	1780-1790	= Delilah (b. 1785/6)
0	persons engaged in [anything]

Listed next to John HALL (100 001 - 120 001 | 010000).

6.  1850 Census Index/Images (online at Ancestry.com; Image #35 of 37):  West Twp., Huntingdon Co., PA, p. 93A, 252/255, enumerated 10 Sep 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Mathew Hall	67	M		Farmer		Md
Delilah  "	64	F				Penna
Mathew   "	21	M		Laborer		"

Matthew's age appears to be too low because all earlier censuses have him born in the 1770s (i.e., he should be in his 70s, not his 60s).  Living between John HALL (æ 44, b. PA, wife Mary — twin daughters, Delilah & Mary), on one side, and Widow Eleanor (CORBIN) CORBIN, on the other side.