Richard did have an older brother called William but he was born c. 1870 not 1880. But really the only way to know whether two people are related is to generate their family trees. The best way to begin here is by creating profiles for your known relatives with links to free sites like familysearch or freebmd.
Here is your Richard in 1891 for example:
"England and Wales Census, 1891," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QFXL-MMM : 2 May 2019), Richard Barnes in household of William Barnes, Surrey, England, United Kingdom; from "1891 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 12, Surrey county, subdistrict, The National Archives of the UK, Kew, Surrey
In 1901 (a few months before his marriage) he's living in Farm Road. The numbers aren't clear from the census but his neighbour William Soper at 21a records a visitor Edith Hall who I would be pretty confident was your great-aunt.