Sindarin adjective meaning “heavy” attested only in the name Mablung “Heavy Hand” (S/185). Given this name’s Quenya cognate Q. Lungumá (VT47/19), S. lung probably developed from primitive ✶lungŭ*, where the [[s|[u] was prevented from become [o] by the presence of the nasal [ŋ]]].
The Gnomish glosses for this word from the 1910s included the more metaphorical senses of “grave, serious” (GL/55). It’s possible the Sindarin word could be used in this way as well.
Conceptual Development: In the Gnomish Lexicon from the 1910s, the word for “heavy” was also G. lung (GL/55), an element in the name G. Mablung as well (LT2A/Mablung). Its primitive form was not given, but judging by the related word G. luntha- “to balance, weigh”, it might have been ᴱ√LUŊU. The form ᴱN. lung “heavy” reappeared in the Early Noldorin Grammar from the 1920s (PE13/122), but became ᴱN. lhung* in the (Early) Noldorin Dictionary (PE13/163), after Tolkien decided that [[en|initial [r-], [l-] were unvoiced]].
In The Etymologies from the 1930s, the Noldorin form of this word was N. lhong derived from primitive ᴹ✶lungā (Ety/LUG¹), where [[n|the [u] became [o] due to a-affection]]. At this point in time, Mablung was Doriathrin/Ilkorin rather than a Noldorin name (Ety/MAP), so there was no conflict.
After Tolkien abandoned the Ilkorin language, Mablung would have become a Sindarin name, and Tolkien needed a new etymology for it. Judging by its later Quenya cognate Lungumá (VT47/19), it seems that Tolkien revised the primitive form of this word from ✶lungā to ✶lungŭ, as describe above, possibly a restoration of its etymology from the 1920s. This meant there was no a-affection in the Sindarin development, making S. lung the Sindarin form of the word.
Neo-Sindarin: I personally prefer S. lung for the Sindarin word for “heavy”, but some Neo-Sindarin authors use the reformed word ᴺS. ^long, based on the Noldorin word lhong in The Etymologies, switching to a voiced [l] because the unvoicing of initial [l], [r] does not happen in Sindarin phonology. This is not entirely consistent with my prefered Neo-Quenya word fof “heavy”: lunga; I assume there was some divergent evolution in Sindarin and Quenya for this word.