wm Beattie would appear to be son of Thomas Beattie + wife mary - however the 1861 census index is totally confusing (+ poorly written - at 4 Fancy St is Thomas a shipwright age 42 born douglas a 9 yr old Mary a scholar but indicated as 'wife@ a son Wm age 11 wks or months - a stepdau Sarah Starky (as best as I can read - there is no obv bapt but a Sarah Starkie marries John Bogie Bra 18680412 + a lodger? Robert Fitzgerald (not Taggart as BL has - interestingly BL makes the same misreading in 1851 census of Taggart for Fitzgerald - the 1851 census for Robt (a nailer at 4 fancy st ) also include a sarah of the same age in that household - all parties in both 51 + 61 indicate born in Douglas (but some census enumerators were idle and never really checked) - interestingly a Thomas Beatty m a Mary Ann Fitzgerald at Braddan 18480510
In 1841 there is a 50 yr old Thomas Beaty (s/o Thomas Beaty + Margt Moore - bapt DSM 17911113) a tailor at spittalls court + wife Mary Kinrade also 50 - in 1851 (misindexed as bratty by BL) at 6 fairy ground with son Wm a ship carpenter age 29.

Best of luck with this one!