Meaning of "owedst"

Solution 1:

This is a second person past tense form of "to owe." To give a parse of the morphology:

owe - d   -  st
owe - past - 2sg

The "-d" or "-ed" is the usual past tense (and participle) marking we know and love today. The "-st" is the second person singular agreement morpheme, which we no longer have in Modern English.

As for its meaning, "owed" sort of makes sense, but this might be a more archaic use for it.

Edit: Here is the advanced search page for Open Search Shakespeare: http://www.opensourceshakespeare.org/search/search-advanced.php

If you select Regular Expression and search .*edst, you'll find a lot more examples with more easily recognizable verbs.

Solution 2:

Apparently there is an archaic sense of 'owe' meaning to possess or to own: owe in merriam-webster. The object of 'Owedst' is the sleep, which the subject enjoyed (or 'owned'), not the concoctions that he could have ingested.

Solution 3:

The "-st" is a verb ending that indicates second person singular. It is still present in contemporary German, for example.

Etymonline says:

owe
O.E. agan (pt. ahte) "to have, own," from P.Gmc. *aiganan "to possess" [...]. Sense of "to have to repay" began in late O.E. with the phrase agan to geldanne lit. "to own to yield," which was used to translate L. debere (earlier in O.E. this would have been sceal "shall"); by late 12c. the phrase had been shortened to simply agan, and own (v.) took over this word's original sense. An original Germanic preterite-present verb (cf. can, dare, may, etc.). New past tense form owed arose 15c. to replace oughte, which developed into ought.