it makes no difference to me either.  i suppose it can be nuked but if you revive it, no big deal either

Along with 重い罪 this is one of two 重いX entries drawn from a kanji dictionary to illustrate 
a less common sense of 重い. GG5 and other EJs have heaps of these 重いX subentries.
I had wanted to keep these two as they are not the usual 重い = heavy cases, but I won't 
lose sleep if they go. I'm adding them to the extras glossing file in wwwjdic.

yes, even eijiro doesn't bother.  more a job for an example sentence than an entry

I think this should go.
任務 is just one of many words that can be used with this sense of 重い. This entry doesn't help someone understand the meaning the 重い地位 or 重い責任 or 重い意味, etc. (And I'm not proposing we create entries for them).

It is sense 4 of 重い, so not so obvious.