There are lots of correlated variables here, so it's difficult to pick out useful information.
The comment thread on the article includes lots of discussion about the impossibility of a wedding that is both cheap and large, but lots of people pointing out that weddings with lots of church and/or community support can be both cheap and large. But church and/or community support are also correlated with other elements of a very stable social structure.
For example, my wedding was both large (> 600 people attended our reception) and cheap (< $3000). How is that possible? We're Mormon, so the actual marriage ceremony was at the LDS temple, which is free, and allows limited attendance. Then we had a wedding breakfast for the ~50 people who attended the ceremony, but the breakfast was at the church (free) and the food was cooked and served by members of our congregation (ingredients cost: low; labor: free). The reception was at the church (free); the bridesmaids paid for their own dresses, best man rented his tux, etc.; the flowers were a wedding gift from a cousin with a flower shop; the table centerpieces and other decorations were handmade by friends and relatives, so we only paid for the materials (cheap); the cake was made by my aunt, who had a wedding business on the side, and cost us $200 for a large, beautiful and tasty cake; my aunt also provided backdrops and other decorations; and some other relatives who are professional photographers did the photos. I don't recall who did the music, but it was all free, using the church's sound equipment. Our biggest expense was the hors d'oeuvres which were actually made by my wife's sisters, so we paid only for the ingredients.
The common thread throughout that list is heavy support from friends, family and community. But I suspect that deep family and church/community support are strongly correlated with long-lasting marriages for lots of reasons which have nothing to do with the wedding day, which to me suggests that those are far more relevant and that wedding cost and attendance are mere proxies for those variables. Also related is the fact that if a lot of people attend, you also get a lot of gifts. So big/cheap weddings are financially beneficial to the couple (mine sure was; spontaneous cash gifts alone -- from the "money tree" -- were more than 2X what we spent, plus all of the gifts of housewares, etc.), while small/expensive weddings are a net drain on their finances.
Similarly, long-term dating tends to be more uncommon among those who get married very young, because it takes time to date someone for 2-3 years, and it's well-known that marriages of the very young are riskier.
Elopement is another one: Those who elope are generally people who decide to get married on the spur of the moment. Such impulsiveness doesn't bode well for future decisions if your goal is long-term stability.
It would be interesting to see a study on this done well, with lots of effort put into teasing apart the correlated variables. This one doesn't actually tell us much.