In honoring and venerating the Blessed Virgin Mary, we worship and honor and adore her Son.
St. Louis Marie de Montfort (one of the giants in the history of Catholic Marian devotion) wrote:
We never give more honor to Jesus than when we honor his Mother, and we honor her simply and solely to honor him all the more perfectly.
Doing Jesus’ will honors Jesus; so does honoring His mother, which (as it says above) is always intended as primarily honor and glory to the Son, Who made His very mother, as He willed. Honoring His mother is honoring Him, in Catholic / biblical both/and thinking.
Stating “we never give more honor” is not saying that it is the highest or only form of honoring Christ; only that no other form could give more honor.
The biblical motif of imitating holy people is similar to veneration (see: Rom 11:14; 1 Cor 4:15-16; 11:1-2; Phil 3:17; 4:9; 1 Thess 1:6-7; 2:9-14; 3:7-9; 1 Tim 4:12; 2 Tim 3:10-14; Heb 6:12; 13:7; Jas 5:10-11; 1 Pet 3:1-2; 5:2-3).
St. Paul makes it clear more than once that imitating him is in complete harmony with the notion of imitating Christ, whom Paul is imitating (see, e.g., Ephesians 5:1: “Therefore be imitators of God, as beloved children:): “Be imitators of me, as I am of Christ” (1 Cor 11:1); “And you became imitators of us and of the Lord . . .” (1 Thess 1:6). It’s not either/or.
By analogy, it is altogether proper to venerate and honor saints, who have more perfectly attained God’s likeness (Matt 22:30; 1 Cor 13:9-12; 2 Cor 3:18; Phil 3:21; Heb 11:40; 1 Jn 3:2; Rev 21:27; 22:14), in light of the example of how “heroes of the faith” are regarded (Hebrews 11) and also the biblical injunctions to honor all sorts of people:
- All men (Rom 12:10; 1 Cor 12:23-26; 1 Pet 2:17).
- The emperor (1 Pet 2:17).
- Government authorities (Rom 13:6-7).
- Fathers and mothers (Ex 20:12; Dt 5:16; Eph 6:2).
- Widows (1 Tim 5:3).
- Elders, preachers, and teachers in the Church (1 Tim 5:17).
- Wives (1 Pet 3:7; cf. Gen 30:20).
King Asa was honored after his death (2 Chronicles 16:14; cf. 21:19, showing that this was a general practice). King Hezekiah was also so honored (2 Chronicles 32:33).
There are many more examples in the Bible of veneration of both men and angels (often as direct representatives of God):
Genesis 18:1-4, 22 And the LORD appeared to him by the oaks of Mamre, as he sat at the door of his tent in the heat of the day.  He lifted up his eyes and looked, and behold, three men stood in front of him. When he saw them, he ran from the tent door to meet them, and bowed himself [shachah] to the earth,  and said, “My lord, if I have found favor in your sight, do not pass by your servant.  Let a little water be brought, and wash your feet, and rest yourselves under the tree, . . .  So the men turned from there, and went toward Sodom; but Abraham still stood before the LORD.
The text in-between goes back and forth, referring to “men” or “they” or “them” (18:9, 16) and “The LORD” or first-person address from God (18:10, 13-14, 17-21) interchangeably, for the same phenomenon and personal / physical / verbal encounter.
Joshua 5:14 “. . . as commander of the army of the LORD I have now come.” And Joshua fell on his face to the earth, and worshiped [shachah], . . .
A “man” is equated with God also in Genesis 32:24, 30. The Angel of the Lord is sometimes referred to as God Himself, but not always; and is venerated. Judges 13:15-22 is a remarkable instance of this, in that it goes back and forth between God (13:16, 19, 22) and the angel of the Lord (or of God) as His direct representative (13:15-18, 20-21 and in the larger passage, 13:3, 6, 9, 13). The angel is honored (v. 17), they fall on their faces to worship (v. 20) and at length the angel is equated with God as His visible manifestation (v. 22). But the difference between the angel and God is highlighted by the angel being described as a “man of God” (13:6, 8) and “the man” (13:10-11). See also 6:12-16, 20-23.
The angel of the Lord is also equated with God (theophany) in Gen 31:11-13; Jud 2:1; but differentiated from God as well, as a representative: (2 Sam 24:16; 1 Ki 19:6-7; 2 Ki 19:35; Dan 3:25, 28; 6:23; Zech 1:8-14).
The Bible, in summary, is quite clear: there is an occasional use of angels or men as direct representatives of God, and they are “worshiped” [i.e., venerated] only insofar as they represent God, as a visual image or object, through whom God is working and communicating. But veneration is strictly separated from the adoration due to God alone (see: Acts 10:25-26; Rom 1:25; Col 2:18; Rev 22:8-9). Everything has to be considered together, as a whole.
All of this explicit biblical evidence is precisely in line with what the Catholic Church teaches. Moreover, “worship” is used in a wider (literary) sense of showing reverence or obeisance to men of authority (in this instance, a king), in 1 Chronicles 29:20:
And David said to all the congregation, Now bless the LORD your God. And all the congregation blessed the LORD God of their fathers, and bowed down their heads, and worshipped [shachah] the LORD, and the king. (KJV)
RSV has: “worshiped the LORD, and did obeisance to the king,” but it is one Hebrew word applied to both.
The Bible tells us to “honor all men” — so we think that the Mother of our Lord Jesus Christ, who was God, is worthy of great honor: above all other creatures. And (as shown above), the ultimate and primary aim in honoring and venerating the Blessed Virgin Mary is to worship and honor and adore her Son.