The entry on flight in the Monster Manual doesn’t elaborate on whether carrying a medium or heavy load actually prevents flight, or it simply slows the flyer down below the
indicated speed (and in the latter case, it doesn’t explain by how much the creature is slowed down). Some of the monster entries do make mention of medium and heavy loads in terms of carrying capacity (griffins and spidereaters, for example). Does that mean those creatures can fly with medium or heavy loads? Is it even possible for a flying creature to get airborne at less that its listed fly speed.
You can use a fly speed only when carrying a light load or less. If your load is medium or heavy, you cannot fly; certain kinds of magical flight, such as a fly spell, don’t have this restriction. Check the description of the flying effect to be sure.
A griffin or a spider-eater can carry a medium or heavy load, but it cannot fly when doing so.
Most flying creatures can get aloft at less than their full fly speeds, provided that they can maintain their minimum forward speeds (see Tactical Aerial Movement in Chapter 2 of the DUNGEON MASTER’s Guide). You also can fly when wearing medium or heavy armor if the weight of the armor (plus everything else you carry) doesn’t exceed your light load rating. The armor still slows you down (page 20 in the DUNGEON MASTER’s Guide has an expanded table of reduced speeds). For example, a balor is a Large creature with a Strength score of 35. A light load for a balor is 2,128 pounds. To calculate that, we must use the tremendous Strength rule on page 163 of the Player’s Handbook and find the light load rating for Strength 25 (the number between 20 and 29 that has the same 1’s digit as 35). This gives us a value of 266 pounds. Since the balor’s Strength is 35, we multiply 266 by 4, which gives us 1,064 pounds. The balor is a Large biped, however, so its carrying capacity doubles (1,064 x 2 = 2,128). A balor can fly so long as it carries less than 2,128 pounds. A breastplate for a Large biped weighs 60 pounds (from Table 7–6 in the Player’s Handbook), so its weight won’t keep a balor from getting aloft when wearing it. Since a breastplate is medium armor, the balor’s base fly speed of 90 feet is slowed to 60 feet (from the table on page 20 of the DUNGEON MASTER’s Guide). Since the balor has good maneuverability, it has no minimum forward speed and can easily fly wearing the breastplate. Even if the balor had poor maneuverability, its minimum forward speed would be 45 feet (half its base speed of 90 feet), and it still could fly at a speed of 60 when wearing the breastplate.
If a creature’s base flying speed is greater than listed on the chart on page 20 of the DUNGEON MASTER’s Guide, just divide the creature’s base flying speed into equal parts dividable by 10 and then add up the reduced values for those base speeds off the chart. For example, if a flying creature with a fly speed of 150 feet wears medium armor and can still get aloft, it can fly at a speed of 105 feet. (Its minimum forward speed, if it had one, would be half the base flying speed, or 75 feet.) The reduced speed of 105 feet was calculated by splitting the fly speed into 70 feet and 80 feet (70 + 80 = 150). At reduced speed, 70 feet becomes 50 feet and 80 feet becomes 55 feet (50 + 55 = 105).
Note that some creatures in the game cannot fly when wearing medium or heavy armor, no matter what their load happens to be (for example, the avariel from Races of Faerûn), so be sure to check the creature’s description for any special limits on its flying ability.