From BiblePortal Wikipedia

Vine's Expository Dictionary of NT Words [1]

1: Ἡγέομαι (Strong'S #2233 — Verb — hegeomai — hayg-eh'-om-ahee )

signifies "to lead;" then, "to lead before the mind, to suppose, consider, esteem;" translated "esteem" in  Philippians 2:3 , AV, RV, "counting;" in  1—Thessalonians 5:13 , "esteem;" in  Hebrews 11:26 , AV, "esteeming," RV, "accounting."

2: Κρίνω (Strong'S #2919 — Verb — krino — kree'-no )

signifies "to separate, choose;" then, "to approve, esteem;" translated "esteemeth" in  Romans 14:5 (twice), said of days; here the word "alike" (AV) is rightly omitted in the RV, the meaning being that every day is especially regarded as sacred. See Determine.

3: Λογίζομαι (Strong'S #3049 — Verb — logizomai — log-id'-zom-ahee )

"to reckon," is translated "esteemeth" in  Romans 14:14 (RV, "accounteth"). See Account.

 1—Corinthians 6:4Account.  1—Peter 2:17 Luke 16:15Exalt

King James Dictionary [2]

Estee'M, L estimo Gr. to honor or esteem.

1. To set a value on, whether high or low to estimate to value.

Then he forsook God who made him, and lightly esteemed the rock of his salvation.  Deuteronomy 32

They that despise me shall be lightly esteemed.  1 Samuel 2

2. To prize to set a high value on to regard with reverence, respect or friendship. When our minds are not biased, we always esteem the industrious, the generous, the brave, the virtuous, and the learned.

Will he esteem thy riches?  Job 36

3. To hold in opinion to repute to think.

One man esteemeth one day above another another esteemeth every day alike.  Romans 14

4. To compare in value to estimate by proportion. Little used.

ESTEE'M, n. Estimation opinion or judgment of merit or demerit. This man is of no worth in my esteem.

1. High value or estimation great regard favorable opinion, founded on supposed worth.

Both those poets lived in much esteem with good and holy men in orders.

Charles Buck Theological Dictionary [3]

Is that high and exalted thought of, and value for any thing which arises from a since of its own intrinsic worth and excellency. Esteem is higher than simple approbation, which is a decision of the judgment; it is the commencement of affection: it is a degree of love for others, on account of their pleasing qualities, though they should not immediately interest ourselves; by which it is distinguished from gratitude. Our esteem of God manifests itself in never mentioning his name without reverence; in bowing the knee; in prayer and praise; in all the several forms of outward devotion, and in quick resentment of any dishonour done to him. Our high esteem or veneration of any man appears in an humble, respectful behaviour toward him, speaking his praises, imitating his excellencies, and resenting his dishonour.

Webster's Dictionary [4]

(1): ( v. t.) Estimation; opinion of merit or value; hence, valuation; reckoning; price.

(2): ( v. t.) High estimation or value; great regard; favorable opinion, founded on supposed worth.

(3): ( v. t.) To set a high value on; to prize; to regard with reverence, respect, or friendship.

(4): ( v. i.) To form an estimate; to have regard to the value; to consider.

(5): ( v. t.) To set a value on; to appreciate the worth of; to estimate; to value; to reckon.

International Standard Bible Encyclopedia [5]

es - tēm ´ (חשׁב , ḥāshabh  ; ἡγέομαι , hēgéomai ): "To esteem" means sometimes simply "to think" or "reckon"; in other connections it means "to regard as honorable" or "valuable." We have examples of both senses in the Bible. The word most often so translated in the Old Testament is ḥāshabh , meaning perhaps originally, "to bind," hence, "combine," "think," "reckon" ( Job 41:27 the King James Version;   Isaiah 29:16 ,  Isaiah 29:17;  Isaiah 53:4;  Lamentations 4:2 ). In  Isaiah 53:3 we have the word in the higher sense, "We esteemed him not." This sense is expressed also by ‛ārakh , "to set in array," "in order" ( Job 36:19 , the King James Version "Will he esteem thy riches?" the English Revised Version "Will thy riches suffice?" margin "Will thy cry avail?" which the American Standard Revised Version adopts as the text); also by cāphan , "to hide," "to conceal" ( Job 23:12 , the King James Version "I have esteemed the words of his mouth," the Revised Version (British and American) "treasured up"); ḳālāh , "to be light," is translated "lightly esteemed" ( 1 Samuel 18:23 , "I am a poor man, and lightly esteemed"), also ḳālal , same meaning ( 1 Samuel 2:30 , "They that despise me shall be lightly esteemed"). In the New Testament, hēgeomaı̄ , "to lead out," is used in the sense of "counting honorable," etc. ( Philippians 2:3 the Revised Version (British and American) "counting";   1 Thessalonians 5:13; perhaps  Hebrews 11:26 , but the Revised Version (British and American) has simply "accounting"); krı́nō , "to judge," is used in the sense of "to reckon" ( Romans 14:5 twice); also logı́zomai , "to reckon" ( Romans 14:14 , the Revised Version (British and American) "accounteth"); hupsēlós , "high," "exalted," is rendered "highly esteemed" in  Luke 16:15 the King James Version, but in the Revised Version (British and American) "exalted"; exouthenéō , "to think nothing of," is translated "least esteemed" ( 1 Corinthians 6:4 the King James Version, the Revised Version (British and American) "of no account").

The following changes in the Revised Version (British and American) are of interest: for " He that is despised and hath a servant, is better than he that honoreth himself and lacketh bread" (  Proverbs 12:9 ), "Better is he that is lightly esteemed"; for "Better is he than both they, which hath not yet been" (  Ecclesiastes 4:3 ), "Better than them both did I esteem him," margin "Better than they both is he"; for "Surely your turning of things upside down shall be esteemed as the potter's clay" (  Isaiah 29:16 ), "Ye turn things upside down!" (margin, "Oh your perversity!"), "Shall the potter be esteemed (the English Revised Version "counted") as clay," etc. - in this connection a forcible assertion of the necessary possession of knowledge by the Creator of man.