The most drastic restriction on the Roman soldier's life was that he was not allowed to marry.

The ban on marriage within the Roman Army was created by Augustus, and was later dissolved in 197 BCE by Septimus Severus. Specifically, soldiers in active duty were not allowed matrimonium iustum, "legitimate marriage."

Specifically the ban is described most directly in juridical papyri from second-century Roman Egypt (e.g. like the document I'm looking at here). Most famous is the Cattaoui papyrus (a collection of excerpts of court proceedings before the prefects of Egypt). The legal consequences of not being able to marry are emphasized throughout those documents.

Why did Augustus create this ban? He completely overhauled the army's structure so this is in direct line with creating a "new" army in terms of service, ultimate rewards and long-service dedication. It has been written that it was a recruitment strategy, especially hoping to create a hereditary military situation, as sons lacking the citizenship would be induced to enlist to receive those rights eventually upon their service. In actuality, there was some increased localization of recruitment specifically in Italy and parts of Gallia. So were there "demographic" reasons for the ban? There have been some that were suggested, but a large proponent of this claim is because the ban seems so anti-Augustan in his commitment in propagating the population of the empire. An interesting claim is that the prohibition was intended to keep Italian women within Italy and not have them move to the provinces in tandem with the soldiers. Another claim is that in this way, the Roman army has a stronger Roman identity, and would not marry or have children with non-Romans, to keep his empire and the people "pure and unsulllied by any taint of foreign or servile blood".

So if they did not marry officially, what did soldiers do regarding family life? Not all entered a form of "marriage" or a long-term relationship with women; alternatives of prostitution and rape seemed to be prominent in the daily lives of soldiers. There is evidence that the Roman government legitimized prostitution to a degree by collecting a tax from it - supporting the institution. Less documented is the soldiers' homosexual relations with their own slaves and male prostitutes that was present and also simultaneously reduced the numbers of children produced by soldiers and their camps.

Soldiers also formed long-term unions with women, that weren't officially recognized by the state. It has been characterized (and often assumed) that soldiers "formed quasi-marital relationships (stable, long-term), with relative social equals." However, it was more of a social union, it was not considered "concubinage", which often happens when there is a situation where marriage is either not wanted or not allowed, but it did have the same lack of state rights. Marital terms were common to refer to their partners, especially in the provinces. Also, importantly it was significant that the soldiers' women have found to have "quasi-dowries", which has social legitimacy as opposed to simply a concubine who would bring no dowry and had no standing as a wife.

Did the state try to normalize or punish any part of these unions? They couldn't be formally regulated, so the state had limited impact on them due to their informal nature. The authorities couldn't do much to these situations and only could affect them by denying the civil rights of a legitimate marriage.

Works Cited
Phang, "The Marriages of Roman Soldiers (13 BC - AD 235)". pp 2-3, 13, 198-199, 230-231, 322, 326-7, 346-348, 385-387