It is always tricky when a family moved between different parishes, as the Barron family appeared to do. (Yes, definitely Barron/Baron/Barren.) Thomas married Cath Looney in Maughold, her home parish, on 9 Nov.1835, and the register records that Thomas Baron was from Bride.
The IGI has an extracted record for Thomas Baron bapt 21 July 1814 Bride, Father: DAVID BARON, Mother: JANE LACE, which fits his age in the 1851 census.

There is a church member's entry (unreliable) for this couple which says that they married in Braddan, and David Barron died 22 SEP 1814 Bride. But in this case Brian Lawson's burial list does have an entry for David BARON buried on that date in Bride. I can't see a decree for him despite his having at least one very young child at the time.

His son Thomas also appears to have died young. The Maughold register has Thos BARON aged 39, of Maughold Street, Ramsey, buried in Maughold on 30 Nov 1853.
His wife Cath BARON aged 42, Maughold Street, Ramsey, had been buried in Maughold on 26 Nov 1853.

I had a look in the 1861 census for the one-month old baby Henry Edward from the 1851 census, and found him in Maughold at Ballagilley, with Evan/Ewan LOONEY Head Wid., 75, Farmer of 10 acres Maughold. With Jane LOONEY Daughter UNM 30 Dressmaker b.Maughold, Mary Ann TEARE Niece UNM 11 Scholar Maughold, and Henry BARREN aged 10, Scholar, Nephew, b. Ramsey. (Actually his grandson.)

Ewan LOONEY son of Thomas Looney & Isable Moore was bapt Maughold Parish Church on 27 Nov 1785.
Ewan LOONEY, 80, Ballacreggan, buried Maughold Mar 13 1866.
Ewan's wife Cath Kennish appears to have died between the 1851 and 1861 censuses: Cathe LOONEY, aged 69, Balla Creggan, buried Maughold 20 Mar 1857?
Their daughter Jane Looney (in the above census) bapt 19 April 1829 Maughold was a sister of Cath's who married Thomas Barron.

Sue