Maybe with some more details, some non-Watts-s can lend a hand.
You have these things in your family tree -- you put them there? Can you explain where they came from, e.g. how you have this Frederick as your Mary Ann's father? Is he named on her marriage or birth certificate? Does her "about 1859" birthdate come from her marriage certificate, a census ...? Can you tell us whom she married, what info you have about her date and place of birth (e.g. from censuses)?
In 1871, a 7-yr-old child is indeed too young to be the son of 60-yr-old Mary, barring a medical phenomenon. But your Mary Ann would have been only 12ish herself.
There don't seem to be matches for any of the children listed, in 1861.
And your 1871 Frederick Watts just doesn't seem to exist before that census! I can't even see a death that matches his age in the next 20 years.
There are Mary Ann Watts births 1857-1861 in Wiltshire in 1857 (2), 1858 and 1859. Do you know which is yours? The birth certificate would certainly be the way to go, to answer your questions about her parents.
... Okay, I see numerous trees that have Mary Ann Watts born in 1859 in Worton, Wiltshire. That is in Devizes, Wiltshire, which would make her birth the one in December quarter 1858 in that reg dist.
http://freebmd.rootsweb.com/cgi/search.plAnd they all have her parents as John Watts 1806 and Merab Romaine/Roman 1804. That seems highly unlikely. Has anyone actually got the birth certificate?? It looks like one or two people have stuck the 1861 census info into their three, and a bunch of people have copied it ... possibly from those charming Anc'y "hints" ...
In 1861, John and Merab (Merah at Anc'y) are in Worton, aged 55 and 57, with children John, 16, George, 10, and Mary Ann, 2. I don't think so. But hadn't you tracked your Mary Ann to there? I don't understand where the idea of Frederick and Mary being her parents came from ...
In 1851 in Potterne, John and Merab had daughters
Mary A, 22
Emma, 14
Merab, 12
Jane, 9
and I would think it most likely that your Mary Ann is the daughter of one of them.
They also have son John, 6, and grandson George, 3 months. I imagine he was daughter Mary Ann's son.
In 1841 in Poulshot, they also had
James, 11
Elizabeth, 9
so more candidates for mother or father of both your Mary Ann and young George.
One of the people with a tree showing John and Merab improbably as Mary Ann's parents has corrected the name of Merab (from Meral) at Anc'y. You might want to collaborate!
Mary Ann's birth certificate will tell you who her mother is, but unless she was the daughter of James, it probably will not tell you her father's identity, unfortunately.
Btw, just in case Merab's age was overstated in censuses and she could have been Mary Ann's mother, I checked:
https://familysearch.org/pal:/MM9.1.1/JQNT-XVWbaptised 1804 Potterne
https://familysearch.org/pal:/MM9.1.1/ND11-6LQchild William baptised 1825 Potterne
https://familysearch.org/pal:/MM9.1.1/NKQ1-BSWmarried 1828 Potterne
https://familysearch.org/pal:/MM9.1.1/XQ3Q-HTC1881 census, Merab Watts, aged 77, shown as mother, in the household with Mary Ann, 22, and her husband Thomas H (Hillier) Brown in bishops Lavington.
But very obviously, the numbers just don't add up. Mary Ann very possibly does name John Watts as her father on her marriage certificate though, and may have thought they were her parents.
... all assuming that this Mary Ann Watts is your Mary Ann Watts!