dress, pretend, disguise, profess
裝 centers on putting on an outward appearance, whether by dressing in clothes or by adopting a false front. The meanings of dress, pretend, disguise, and profess all flow from this idea of presenting a crafted exterior.
裝 combines 衣 (clothing) with 壯, which likely contributes the sound and the idea of strength or adornment. The character originally referred to dressing or adorning oneself, and later extended to pretense and disguise.
The bottom 衣 is clothing, and the top 壯 suggests strength or display. Picture someone putting on a strong, impressive outfit to dress up or pretend to be something they are not.
For ソウ, imagine sewing a costume: sew -> ソウ, and you dress up in the finished garment.