Larged-doesn't exist. such a word doesn't exist
largening-we don't say largening, we say an enlarging. object is still in the process of becoming big or huge; it hasn't completed the process.
larger-it is a comparative form of the verb; meaning it is a little more than large
largest-it is a superlative form of the verb. nothing can exceed this object in being large. it is the highest degree of comparison