Neither does the spell description provide any rules that would increase the weight that can be dragged above the weight that can be carried; nor do the rules apply which let characters drag double their carrying capacity. Therefore, the weight detailed in the spell description limits dragging as it does carrying.
The spell description does not talk about dragging
The spell description of mage hand gives multiple examples of what the hand can or cannot do. None of those are related to dragging, except the capability to
manipulate an object
which can be interpreted as including dragging. In the end, there is no specific information about dragging, suggesting that no extra rules (such as increased dragging capacity) apply.
Rules for carrying and dragging apply to monsters and characters with a strength score.
The rules on carrying capacity are found under Using each Ability (PHB p. 175):
Every task that a character or monster might attempt in the game is covered by one of the six abilities.
Neither is the mage hand a monster or character, nor does it have abilities or ability scores. Carrying, specifically, is explained under Strength (PHB p. 176):
Carrying Capacity. Your carrying capacity is your Strength score multiplied by 15. This is the weight (in pounds) that you can carry, which is high enough that most characters don't usually have to worry about it.
Push, Drag, or Lift. You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score). While pushing or dragging weight in excess of your carrying capacity, your speed drops to 5 feet.
All these explanations consider creatures with a strength score. The mage hand does not have these properties. Specifically, these rules state that a strength score entitles a creature to have a carrying capacity and a dragging capacity. These rules do clearly not entitle the mage hand to anything a priori.
A case could be made, that a carrying capacity implies a dragging capacity. However, RAW, this does, a priori only apply to monsters / characters with a strength score, especially so, since the dragging capacity restates the reliance on a strength score.
In the end, it seems like the mage hand's carrying capacity (which is not even specifically declared using that term) is gained another way, i.e. the spell's description which the rules from PHB p. 176 do not apply to. Therefore, the mage hand does not gain increases dragging capacity and cannot drag more weight than it can carry.