If you use the accusative - "Vaše slova vážím", it means "I'm weighing your words (on some scales)." Adding the "si" here doesn't change the meaning much - "Vaše slova si vážím" - "I'm weighing your words (for fun / for my pleasure / in my spare time)".
Only "vážit si + genitive" has the meaning "to appreaciate something"
Vždyť o tom píšu hned vedle v odpovědi uživatelli BoneheadBass. Sloveso weigh má jiný význam, vážit podobně jako "zvažovat, uvážit".
weigh: to think carefully about (something) in order to form an opinion or make a decision, to consider carefully especially by balancing opposing factors or aspects in order to reach a choice or conclusion : evaluate <weighing her options>
Příklad s your words:
"I weigh your words against the words of this youth. I judge in each instance by your respective conduct, and, I am sorry to say, you are guilty." = poměřuji s, srovnávám s