It's a basically a long standing fact that heteronormative couples are far more likely to move because it would improve the husband's career than the wife's. The long standing assumption is 'cause of old school "provider" mentality, but Alan Benson (Carleson School of Management, University of Minnesota) argues it's because often the guy is in a field that's locked to certain locations on earth (like oil fields) whereas the woman is in something that can be done anywhere (like teaching).
In his paper "Re-Thinking the Two-Body Problem: The Segregation of Women into Geographically Dispersed Occupations" (Demography 10, 2014) and there's a full-text draft from 2011 (which this post is mostly going to be based on) Benson looked into how often single men and women moved for work to try to tease out the effects of marriage and he looked at the sort of jobs men and women tended to go for (self segregation) to try to figure out the effect of job choice. He analyzed highly educated workers independently of low skilled workers to account for the effect education/skill may have on the availability of and choice in jobs.
His basic method of analysis is by ranking jobs by how tightly linked they are to a place-geographically clustered to geographically dispersed-by looking how jobs are distributed all over the US. Using census data from 1980, 1990, and 2000, he estimated the employment share of each occupation in each metropolitan statistical area-basically, how many people in this region are doctors, lawyers, casino cage workers, but normalized (a kind of weighing to factor in that there are more teachers than rocket scientists everywhere) by how many people in the US are doctors/lawyers/etc-to figure out which jobs are super tied to a region vs. which ones are kinda everywhere. He found that generally jobs stayed more or less constant with respect to geographic clustering/dispersion.
I [Alan Benson] define married couples as couples where both heads are married with a present spouse. I examine relocation incidence for workers younger than 35 to focus on those most at-risk of marriage and work relocations. Occupations are matched on the occupation in the previous year (i.e. for those relocating, I use occupations prior to relocation). The CPS asks households whether they relocated in the prior twelve months. Those that report doing so are asked for the primary reason for relocation. I define a "work relocation" as a change in residence across counties in which the respondent cites work or job transfer as the primary reason for relocation. Common reasons include relocation for family, upgrading housing, or change in marital status. Relocations "for work or job transfer" include about 10% of relocations.
Benson found that among never married people, men tended to have higher mean clustering scores (meaning that they tended to be in more geographically locked jobs) at a rate that was statistically significant. He also found that single women in jobs that were more geographically locked tended to relocate far more often than single women in non-geographically locked jobs (which support his thesis that it's the jobs, not gender 'causing people to move). He then looked at which gender tended to go into geographically locked jobs, and found that those jobs tended to be overwhelmingly male.
Now of course, looking the list, there's the argument that the gender imbalance of the geographically distributed jobs is itself rooted in sexism. Women tend to not go into STEM fields 'cause they're a minefield and men tend to not go into teaching 'cause it's traditionally viewed as women's work (and people often think they're pedophiles). Women could also be choosing flexible careers in order to have the ability to move should their husband's career require it. The geography dynamic doesn't change significantly when isolated to jobs requiring degrees.
So what if you wanna go all nah and break the system? Well...
Benson (2011) finds that women who enter constrained occupations disproportionately suffer lower earnings, later marriage, and higher divorce rates than men in those occupations or women in flexible occupations.