Obsessing rhymes with:
assessing, reassessing, recessing, acquiescing, addressing, assessing, blaesing, blessing, caressing, coalescing, compressing, confessing, depressing, digressing, distressing, dressing, expressing, guessing, hessing, impressing, lessing, messing, oppressing, possessing, pressing, professing, progressing, reassessing, recessing, redressing, repressing, stressing, suppressing, transgressing
Obsessing sounds like:
obsessions, officemax, opposing, ovshinsky