to weigh  - pesar, tener importancia, contar, considerar, sopesar 

to be heavy

to consider  - considerar, pensar en, tener en cuenta, estimar 

to think over  - ponderar, considerar 

to weigh heavily

to be a burden

to carry weight

to have bearing

to grieve  - afligir, entristecer, apenar, sufrir, afligirse 

to sadden  - entristecer