Heaved rhymes with:
achieved, aggrieved, believed, bereaved, conceived, deceived, grieved, interleaved, misconceived, misperceived, peeved, perceived, preconceived, received, relieved, retrieved, sleeved, unrelieved, weaved
Heaved sounds like:
habit, habitat, haft, hafta, haupt, heaped, hebda, heft, hefti, hefty, hibbett, hobday, hobdy, hoeft, hoevet, hoofed, hoped, hopped, hopwood, houpt, hovda, hovde, how-about, huffed, hyped