We're curious about non religious affiliated items (white dresses, wedding bands, engagement rings, groomsmen / bridesmaids, etc.) My new wife and I were curious - thanks!
I can tell you about the white dress!
Most women in the 18th century were generally married in the best, most formal gown that they had. Royal brides did, however, wear silver and white. For example, Charlotte of Mecklenberg-Strelitz married George III in 1761 in "a Silver Tissue, stiffen-body'd Gown, embroidered and trimmed with Silver, on a her head a little Cap of purple Velvet quite covered with Diamonds ..." (quoted in Anne Buck, Dress in Eighteenth Century England). Even aristocratic, non-royal women could be described as wearing "bridal white and silver". And even some non-aristocratic women were described in textual accounts (some fictional, some not) as wearing white silk or white muslin for their weddings. So the connection of white to weddings was there, but there doesn't appear to have been a very common expectation of wearing it.
When white became the most fashionable color around the turn of the century, ordinary women started to wear it for weddings just as they wore it for formal and informal occasions, if they could afford to. It's always hard to say if an attribution of provenance to a garment is correct, but there are a lot of white muslin dresses (especially embroidered ones) from this period that are said to have been worn by this or that woman for her wedding.
As colors came back into fashion toward the end of the 1810s, fashion plates labeled "wedding dress" continued to show white gowns, and would continue to do so indefinitely. Fictional references also continued to describe women in bridal white. Some will say that this comes from Queen Victoria's wedding, but as you can see from the dates, it's not. Victoria's wedding really had very little effect. Throughout the 19th century, the tradition of wearing a very nice but not white dress persisted for most women, even ones that could afford nice silk gowns. The number of white wedding dresses increased towards the end of the century, and then seems to have exploded around the turn of the 20th with the rise of ready-to-wear and the second vogue for sheer, unlined white dresses. While you can find individual cases of non-white wedding dresses after this, mainly for exceptional circumstances (weddings soon after a death in the family, divorcées, etc.), it had become set in stone that you must be married in white or off-white.