One of my players obtained a helm of comprehend languages. But I cannot find a place in the DMG where it says the weight of the item. Am I missing something here? The character wearing the item is close to his maximum weight carried without being encumbered.
The level of abstraction isn't that granular
On a strict reading of the rules, unless the rule (item description) indicates that a particular item has a weight/encumbrance you don't have to assign one. While some older versions of the game indicated that magical items had (or could have) less encumbrance/weight than a mundane item, this edition doesn't take the details down to that level.
It is worth noting that encumbrance is a variant rule (p 176 PHB), which argues for the DM to go with "master of rules" mode (DMG p. 5) and either choose to make it matter or not. Should it weigh more or less than a shield? A sword? A dagger? Pick an item that makes sense to you, adjust for however much magic might mitigate that, and assign a value.
If you take a look at the armor table (PHB p. 145) you will note that helmets are not a separate item. If your player character is wearing armor that would usually include a helmet (plate is the only one described that way) the helm could act as replacement with no need to assess weight or encumbrance. (The helm of comprehend languages is magical ... as a DM, it's your call).
The simple answer:
If an item doesn't list an encumbrance/weight, it doesn't have one (benefits of magic). Play on.
If it is important to you as DM to include encumbrance on everything, as you are using a variant rule, assign one. Play on.