Only one instance of each durational spell can affect the same target. A sorcerer cannot, for example, cast Vorpal Blade twice and enter combat with two such weapons or a single stronger Vorpal Blade. Similarly, casting the second Weaken spell on a target already weakened by the first casting would not make that target any weaker.
However, different spells can have the same target, so a sorcerer wielding a Vorpal Blade would benefit from the Armour spell, and the same spell can be cast on different targets, so a sorcerer could Weaken multiple opponents with repeated castings of the spell.
Spells that gradually decline in strength or effectiveness over time, such as Wall of Magic may benefit from being recast before they expire, as this reinvigorates them back to maximum effectiveness.