The box was too big and awkward, so I put these in a bag and brought them.
嵩張る is actually a good free translation and I like it. But 嵩張る doesn’t have a meaning of “awkward”. I think it’s better to change the English translation rather than change the Japanese one.
嵩張る is not usually written in Kanji but in Hiragana. 嵩 is registered as one of the 常用外漢字, which is highly recommended to rewrite in Hiragana.
かさ basically means “volume”. 大雨で水かさが増した (おおあめでみずかさがました), for example. means “the heavy rain swelled the water of the river.”
かさばる or かさ張る means “to consume a large space to have it”. 膨張する (ぼうちょうする) means “to swell”. I hope you all get the nuance of 張る.