Why does "that" appear at the end of the fragment?
"That" is used here to connect the phrase that follows ("with some heavier days later on"). It is not the end of the actual fragment, and "that" is followed by a comma "," to give pause and break down the sentence into more digestible chunks, as the full sentence is quite long and contains more than one idea. In this sentence, "that" can also be preceded by "so" but the speaker has chosen to omit this word. The sentence meaning does not change with the omission of "so" here.