Gradually and progressively:
— His health weakened day by day.

synonym: daily.

Roget 104: repeatedly, often, again, anew, over again, afresh, once more; ding-dong, ditto, encore, de novo, bis^†, da capo [It].    again and again; over and over, over and over again; recursively [Comp.]; many times over; time and again, time after time; year after year; day by day &c.; many times, several times, a number of times; many a time, full many a time; frequently etc. 136.    ... show more

Roget 106: while, whilst, during, pending; during the time, during the interval; in the course of, at that point, at that point in time; for the time being, day by day; in the time of, when; meantime, meanwhile; in the meantime, in the interim; ad interim, pendente lite [Lat.]; de die in diem [Lat.]; from day to day, from hour to hour &c.; hourly, always; for a time, for a season; till, until, up to, yet, as far as, by that time, so far, hereunto, heretofore, prior to this, up to this point.    the whole time, all the time; all along; throughout etc. (completely) 52; for good etc. (diuturnity) 110.    hereupon, thereupon, whereupon; then; anno Domini, A.   D.; ante Christum, A.   C.; before Christ, B.   C.; anno urbis conditae [Lat.], A.   U.C.; anno regni [Lat.], A.   R.; once upon a time, one fine morning, one fine day, one day, once.    ... show more

Roget 138: periodically etc. adj.; at regular intervals, at stated times; at fixed established, at established periods; punctually etc. adj.. de die in diem [Lat.]; from day to day, day by day.    by turns; in turn, in rotation; alternately, every other day, off and on, ride and tie, round and round.    ... show more