This is a tough question to answer, because burial and inheritance practices changed a lot through the thousands of years of European history. I can give a few pieces of the puzzle:

It was very common for men to be buried with weapons between the 5-7th centuries in most of North Europe. This practice lasted much longer in Scandinavia. This was really common - in England, about 45% of the men buried between 450-650 had at least one weapon in their grave (usually a spear, less frequently a sword and/or shield; see Härke 1992).

It's not always clear why weapons were put in the grave. The thought used to be that every man with a weapon had been a warrior, but lots of children and men born with handicaps that would have made it difficult for them to fight were also buried with weapons (Härke 1990). So a lot of historians and archaeologists have suggested that being buried with weapons meant you were part of the ruling warrior class rather than being an actual warrior yourself (eg Halsall 2003). For a long time, it was suggested that men were buried with weapons so they could fight in Valhalla (see Härke 2014 for a discussion of this theory) - but all of the texts that describe Valhalla were written many centuries after people were being buried with weapons, so we're not sure if this was actually part of their religion or not. It's also possible that people were buried with weapons to make them appear wealthy or important (to impress the neighbors at the funeral; Theuws 2009). See Härke 2014 for more suggestions why weapons were included in men's graves during this period.

After the seventh century, fewer and fewer men are buried with weapons in Northern Europe. We're not entirely sure why: the common argument was that it was because they became Christians, and Christians didn't believe in burying the dead with weapons and other stuff (but this argument has been soundly debunked, see Rebillard 2003, Effros 2002, Halsall 2010, Hadley 2001 - to name just a few). Instead of burying men with weapons, the families of dead men were often required by law to give their weapons back to the local lord (Hadley 2001). Presumably, the lord would then give new weapons to the dead man's heir after the heir swore his oath of loyalty to the lord (see Le Jan 2000).

That's the period I study. It can be summed up as:

450-650: Northern European men are often buried with weapons. Many of these men were probably not warriors; it was just a common way to bury a man.

After 650, men are often required to return weapons to their lord.

But then this changes later in the middle ages, and I'm pretty sure you again see men being buried with weapons - but I'll have to leave it to someone else to talk about that, because it's later than I study.

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Sources:

Effros, Bonnie. Caring for Body and Soul. Pennsylvania State University Press, 2002.

Hadley, Dawn. Death in Medieval England (Tempus, 2001).

Halsall, Guy. Warfare and Society in the Barbarian West, 450-900. Routledge, 2003.

Halsall, Guy. Cemeteries and Society in Merovingian Gaul: Selected Studies in History and Archaeology, 1992-2009. Brill, 2010.

Härke, Heinrich. Angelsächsische Waffengräber des 5. Bis. 7. Jahrhunderts. Rheinland-Verlag GMBH, 1992.

Härke, Heinrich. "Warrior Graves? The Background of the Anglo-Saxon Weapon Burial Rite." Past and Present 126 (1990): 22-43.

Härke, H. 'Grave goods in early medieval burials: messages and meanings', Mortality 19:1 (2014), pp. 1-21. You can read this article at: http://tinyurl.com/lc2yrve

Le Jan, Régine. 'Frankish Giving of Arms and Rituals of Power: Continuity and Change in the Carolingian Period.' In F. Theuws and J. Nelson (eds), Rituals of Power (Brill, 2000), pp. 281-310.

Rebillard, E. The Care of the Dead in Late Antiquity (Cornell, 2003).

Theuws, Frans, and Monica Alkemade. ‘A Kind of Mirror for men: Sword Depositions in Late Antique Northern Gaul.’ In Rituals of Power: From Late Antiquity to the Early Middle Ages, ed. by Frans Theuws and Janet L. Nelson. Leiden: Brill, 2000, 401-476.