This is the 327th most frequent German word.
schweren
"Schweren" means "to make heavy" or "to weigh down."
Here, "schweren" is used as an adjective to describe an object (suitcases) as having a considerable weight.
Er trug die schweren Koffer allein.
He carried the heavy suitcases alone.
In this sentence, "schweren" describes losses metaphorically, as severe or grave, hence conveying emotional weight.
Nach seinen schweren Verlusten entschied er sich, Hilfe zu suchen.
After his grievous losses, he decided to seek help.
The word "schweren" is used here adjectively to characterize a time period as challenging or arduous.