weigh down vs press down on

weigh down and press down on both are verbs.

Word	Noun	Adjective	Verb	Adverb
weigh down	No	No	Yes	No
press down on	No	No	Yes	No

As verbs, weigh down and press down on are synonyms defined as:

Other synonyms of weigh down include bear down, bear down on, drag down.

weigh down (verb)	press down on (verb)
exert a force with a heavy weight	exert a force with a heavy weight
be oppressive or disheartening to