From the second edition (1989):
sup, n.1
(sʌp) Forms: α. 6– sup, 6–7 suppe, 7 supp. β. 7 soope, 7–8 (9 dial.) soop, soup, (8 Sc. soupe, 9 dial. sowp, zoop). [f. sup v.1
There is no evidence of continuity with OE. súpa (cf. MLG. sûpe, early mod.Du. zuipe, Du. zuip, ON. súpa).

The isolated instance of sense 2, unless it be a misprint, is difficult to account for.]

1. A small quantity of liquid such as can be taken into the mouth at one time; a mouthful; a sip. (Also in fig. context.)

α 1570 Levins Manip. 189/37 A Suppe, sorbillum. 1621 Fletcher Pilgrim iv. i, I'le bring you a sup of Milk shall serve ye. 1657 J. Watts Scribe, Pharisee, etc. iii. 71 A sup of wine (as a morsel of bread) may do well enough. 1710 Brit. Apollo III. No. 47. 3/1 To see his Brave Army Engage; And to Swallow up, The Allies at a sup. 1719 De Foe Crusoe i. (Globe) 82, I went to my little Store and took a small Sup of Rum. a1764 Lloyd Fam. Ep. to J. B. Poet. Wks. 1774 II. 40 With so much wisdom bottled up, Uncork, and give your friends a sup. 1840 Thackeray Paris Sk.-bk. v. (1872) 49 Taking a small sup at the brandy~bottle. 1872 Calverley Fly Leaves, On the Brink ix, A sup Of barley-water. 1888 W. S. Gilbert Yeom. Guard i, Who sipped no sup, and who craved no crumb.
β 1633 Orkney Witch Trial in Abbotsford Club Miscell. 152 The powre woman sent in to the said Robertis house, and got ane soup off milk from his wyff. 1662 Tuke Adv. 5 Hours i. 10 A soop of Chocolate Is not amiss after a tedious Journey. 1667 Dryden Tempest ii. i, Here's another soop to comfort us. 1719 D'Urfey Pills (1872) III. 7 I'll take a full Soop at the merry Milk-pail. 1785 Burns Cotter's Sat. Nt. xi, The soupe their only Hawkie does afford. 1818 Scott Rob Roy xviii, It's the part of a kind son to bring her a soup o' something that will keep up her auld heart. 1851 Sternberg Northampt. Dial., Soop, a sup, drop.

b. Phr. (a) bit (later bite) and (a) sup, a little food and drink. So bit or sup, neither bit nor sup.

1665 in Verney Mem. (1904) II. 244, I save [? have] a bitt and supp bye myselfe 2 owers after them. 1818 Lady Morgan Autobiog. (1859) 148 The moment‥we had swallowed our ‘bit and our sup,’ out we sallied. 1865 G. Macdonald Alec Forbes 15 I'll tak her in wi' my ain bairns, an' she s' hae bit and sup wi' them. 1880 Browning Dram. Idylls Ser. ii. Pietro of Abano 233 Lodging, bite and sup, with—now and then—a copper‥is all my asking. 1902 V. Jacob Sheep-Stealers ix, The pleasant offer of a bite and a sup.

c. transf. Drink. dial.

a1810 Tannahill Poor Tom Poems (1846) 109 Poor Tom loves his sup, and poor Tom is despised. 1876 Whitby Gloss., Sup, Suppings, Sups, drink of all kinds.

d. a good sup: a fair amount, a considerable quantity (of liquid). dial.

1601 Archpriest Controv. (Camden) II. 173 If a cow give a good soope of milke, she is to be thanked. 1848 A. Brontë Agnes Grey i, [Of a fall of rain] It's comed a good sup last night too. 1872 Hartley Yorksh. Ditties Ser. i. 97 They reckon to brew a gooid sup o' ale in October.

2. = sop n.1 1. Obs. rare.

1543 Traheron Vigo's Chirurg. ii. viii. vi. 82 He muste‥eate a sup or shewe made with grated breed & almandes [orig. panatellam fariolam amigdalatam‥confectam].