The speed of a character or unit can depend on the personal statistics of the character or unit and the class of the unit. For example, a Knight is going to have naturally slower speed than a Myrmidon, so a Myrmidon is naturally more likely to double attack and evade a counterattack in a fight against the Knight. However, the concept of Constitution makes this slightly more complex; if the weight of a weapon is higher than the unit's Con, the unit will suffer from a speed penalty. Weight-Con = Speed Penalty. For example, if a Pegasus Knight with a Con of 5 uses an Iron Lance ( Wt. 8) to attack an enemy she will suffer from a penalty of 3 Speed. What is left is her Battle Speed. If her Battle Speed is 4 higher than the enemy's, she will double him.
A Speed Ring or a Speedwing can be used to raise the speed of a character. Of course, the number of speed-boosting items present in each game are limited, so often they are used to boost the speed of a character with low speed, helping their evasion and their chances of double-attacking. Brave Weapons are also affected, if their speed stat is 5+ from their opponent, they shall attack 4 times instead of 2.
In modern Fire Emblem games, such as Fire Emblem: Path of Radiance or Fire Emblem: Radiant Dawn, the Strength Stat is used in place of Constitution to determine the penalty, and Fire Emblem Awakening discards the Speed Penalty entirely.