There were two types of theatres in England c. 1600: the open-air, mosh pit ones that we stereotype as Elizabethan; and enclosed, indoor ones. Although it's possible that some theatres may have had windows to let in some light (there are occasional references to windows being shuttered), candles were the primary indoor light source for late medieval and early modern theatre. In general, outdoor performances attracted a wide range of audience members and were quite affordable; indoor playhouses were reserved for the rich. Often a playwright would have a specific type of theatre/audience in mind when writing, although plays could be--and in Shakespeare's case, generally were--performed in both types of setting.

First, we have civic ordinances from various cities regulating traveling acting companies (who might also perform at a major theatre if there was one). Not being able to perform "by candlelight" (i.e. at night) makes a frequent appearance if the town appears concerned with noise (usually there will also be a prohibition on music or drums). Everyone's favorite diarist Samuel Pepys confirms this was the case for London, when he notes his amusement that one actor needed to "suppose it to be dark, and yet he is forced to read his part by the light of the candles."

Second, theatre costumes generally used fabric in colors meant to catch the candle light (as Francis Bacon explains specifically) as well as possible. The court masques that overlap with indoor theatre in more ways than one--including secondhand costumes--were performed by candlelight and give very specific directions about costume color.

Finally, as Martin White traced, plays that we know were intended for a indoor audience, an outdoor audience, or both have different ways of dealing with day/night scenes. While there must always be some light, so actors have to act the full darkness, plays intended for an indoor theatre do not swap quickly back and forth between day and night scenes. It would take too long to light and snuff enough candles! Instead, there are usually more gradual shifts, or an entire act pause while the crew relights the rest of the candles following a night scene. In parallel, scenes set at night often refer explicitly to some kind of candle or torch, which would have helped signal to an open-air, daylight-only audience that the stage was supposed to be shrouded in darkness.