If this is a recent development, then our starting point is, basically, today. What is "marriage" today?
A socio-legal contract between two individuals, previously of separate gender but today of any gender, that establishes the relationship between the parties for the purpose of protecting earnings, assets, and the parental rights over children/minors.
A socio-religious agreement between two individuals, still predominantly of separate gender (but this is changing), that establishes the credibility of the relationship within the religion and within society in general. I'd need to do some research into it, but my gut feeling is that a religious marriage is today still deemed "more credible" than a marriage by civil authority (but I honestly admit that may be an ignorant bias due to my own religious upbringing.)
A culturally-based commitment between two (or more) people for emotional and/or economic benefit (aka, "living together"). Some localities consider a long-term commitment to this kind of relationship to constitute a "common-law marriage," meaning that eventually legal protections and expectations attach to the relationship due to the long-term commitment looking a whole lot like a civil or religious marriage.
And at the other end of the scale... we have "shacking up," which can be a serious relationship with emotional and economic benefits, but can also be nothing more than a long-term "one night stand" where little is gained other than cheaper rent and a readily available date.
Where would a parthenogenic party fit in all this?
Such a person would still have been raised in the culture of "marriage" (aka, all that variety above) with locality-specific shifts due to culture (is our subject from one of the so-called "western civilization" countries? or would she be from an African or Australian tribe? etc.). The specific origin of our subject is not defined in your question, but it is important. A parthenogenic woman raised in Iran would have a very, very different set of choices compared to a similar woman raised in Berkeley, California.
However, we could make some simple assumptions
Using western culture as our starting point (I'm most familiar with it), and ignoring the more interesting unions (polygamy comes to mind), let's consider some of the "cultural pressures" that would affect the decision.
Shared Economics: Unless one happens to come from a wealthy family, it's almost impossible today to raise children on a single income.
Shared Chores: I've worked with single mothers who were raising their children, not only without a partner, but in a culture that doesn't regard single women highly. One such lady related a story of watching happy families driving to church services while she was outside chopping wood because there simply wasn't enough time to both chop the wood for heat and make breakfast and take care of her child to make it to services (which she dearly wanted to do).
Shared Emotional Strength: Humanity is a social species — and not simply because of the biological drive to propagate the species. We like to be together, to share experiences, to shout together in joy and to cry on one another's shoulders. Yes, there are the exceptional people who can live their lives alone on a deserted island and be entirely happy — but that would drive most of us bonkers. Few things are worse than achieving a victory and having no one to share it with who is totally invested in that victory and the individual's part in it.
And on top of this are...
Legal benefits and consequences to a recognized relationship. Here in the U.S., our tax structure has a "marriage penalty" (this, despite some circumstances that make marriage beneficial for taxes).
Social benefits and consequences relating to the children. While a great many children attend school having only one parent, having two is still considered culturally preferred.
Social stigma of both the parent and the child. This one will be one of the more powerful issues, but also the more difficult to define. Humanity is very good at not liking things that are "outside normal." It's a funny behavior, because "normal" has more to do with the habits and cultural perspectives we learned as children than they do an actual statistical average. Nevertheless, parthenogenic families can expect bias... even hatred... because they're outside of what the culture generally considers "normal."
And that issue deserves a bit of detail. The U.S. has taken great steps to recognizing a considerable amount of diversity, which could be said that we're redefining "normal" to have little or no meaning at all. Nevertheless, only a blind idiot doesn't recognize that the powerful habits of previous generations (male-female marriage, for example) are not at all gone... they've simply gone underground where the vocally violent supporters of both sides can't easily hear one another. In many ways, the nation is as divided as it has ever been — only the socially-acceptable public voice has changed. There's still a lot of work to do.
TL;DR, what's your point, JBH?
Marriage, meaning a meaningful and committed relationship (whether formally sanctioned with a piece of paper or not) will remain a significant component of parthenogenic families if only out of habit. All those non-sexual/non-reproductive benefits (and consequences!) still apply. And while after some time the world may recognize the non-necessity of a reproductive partner, it may never relax the economic, legal, and emotional conditions that tend to drive people together.
And on top of that, unless parthenogenesis results in an individual being substantially inhuman, that person is still a very social "being alone stinks" person.