In E. A. Abbott's A Shakespearean Grammar you will find his entry:
Omission of Thou. (See also 399, 402.) After a verb ending with the second person singular inflection, the thou is sometimes omitted in questions, as:
“Didst not mark that?” (Othello, ii. 1. 260.)
In A Modern English Grammar on Historical Principles (Otto Jespersen, 2013), Volume 3, it is explained that:
The frequent omission of thou in questions (in EIE and
later in archaic style or dialect) as in
Art mad? = Art thou mad?
was explained 1.6.36 from the purely phonetic dropping of the
weak vowel, after th had been assimilated to the preceding t: art /ou > art-te, arte > art, etc.
- Gammer 104 Art deffe.. why canst not heares [ = hear us]
- 122 Canst not learn to-night, man? Seest not what is here?
- Marl J 1930 Wilt drinke?
- 1956 hast been in Malta long?
- 1958 Dost not know a Iew?
- Sh Gent III. 1.390 Why didst not tell me sooner?
- Lr IV. 1.29 Fellow, where goest?
- Cy V.5.110 Know'st him thou look'st on? speak! Wilt haue him liue?... Wherefore ey'st him so?
- Byron 572 Art sure of that?
- Lamb R 11 Dost hear, girl? Why don't you answer?
- GE A 2 dost think thee'st finished?
- Bennett C 2.44 Who'st been running after?
The introduction to a 2003 edition of The Reformation (a play written by Joseph Arrowsmith in 1673) sheds some light on the contexts in which the ellipsis of thou can be used and on the connotations it can convey:
The use of thou required verbal forms ending in -st (e.g., comest or com t) or -rt (art, wert). Although the presence of the subject has always been obligatory in English sentences since the early modern period, the distinctiveness of these endings could at times lead a writer to dispense with the pronoun, especially in interrogative sentences in which the pronoun should have followed the verb (see Barber 200). In The Restoration, this kind of ellipsis had already become archaic, but in Arrowsmith’s play it appears several times, in conversations in which a character displays an extreme degree of familiarity: most instances belong to speeches by Lysander and Juliana in which the speaker expresses his or her affection or concern for the person addressed (e.g., in combination with terms of endearment, as in Juliana’s
“Poor innocent, do’st think that love’s the only cause?” before Lelia, 1.2.21;
“Ar’t’ come, dearest?” before Lysander, 3.3.18).
Some of these, however, are feigned expressions of affection, or appear in the context of mock-heroic discourse, to the extent that it is difficult to ascertain whether the ellipsis of thou should ultimately be regarded as a device with mocking overtones.