My area of historical interest is the Baltic region, so speaking to that effect it depends.

Generally I would say that germanic eastward expansion had a distinct divide. In Poland you see an accepted baptism in 966 AD which prevented a mass transportation of colonists into the region.

In what became Prussia you see this eastward expansion involving colonists and resistance and eventual subjugation of the local populace (called baltic or old prussians in some sources). The Ostsiedlung as it is called in the german language (and some english language sources as well) sort of stopped in Prussia.

In Livonia (modern day Latvia and Estonia) you see a migration of the north germanic power structure, clerics, knight orders ect to the region, but you do not see a migration of colonists in the same way as you do in Prussia.

In the baltic region over-population in germanic principalities to my knowledge was never really a concern. The historiography generally defaults to debates about economic or religious motivation. Though some more modern scholars seem to take a synthetic approach to this idea.

If you are interested in reading more I would recommend the Archaeology of the Prussia Crusade (by Pluskowski) concerning Prussia and the 2006 paper Profits of the Cross by Munzinger. If you want a whole book on the Baltic area in the medieval ages your best bet would be to read Henry's Chronicle of Livonia and a book about the Danish impact probably the Bysted volume (jerusalem in the north).

edited to mention if you want more information about Poland (though it is only tangentially relevant) read the Norman Davies 2 volume work on Poland its called God's Playground, but you only need to read the first volume if your only concern is the medieval era.

The argument might have some tenuous links to the prevalence of third, fourth etc. sons who were from noble families but were unlikely to ever inherit the lands or titles and did not want a career in the Church. Similarly to the English conquests of Wales and Ireland, if they went on Crusade then there was a real opportunity for social advancement by establishing themselves as the new nobility of the Levant. Although the Crusade was truly huge, however, it represented nothing but a tiny fraction of the population of Europe, which during this period still had plenty of essentially empty land.

(Tyerson, God's War)