press down on vs weigh down

press down on and weigh down both are verbs.

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

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

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

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