The use of "weigh" is fine in all three sentences (but the tenses in the first sentence don't agree). The insertion of "a" in #2 is a consequence of the use of "mere", not specifically anything to do with "weigh". The same pattern arises with "mere" with all verbs that can be used to indicate a quantity: "He earns $10,000 a year" -- OK "He earns a mere $10,000 a year" -- OK "He earns a $10,000 a year" -- Wrong I'm not aware of any differences here between American and British English.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
exodejavu
Given that I change "mere" to "merely," the "a" should be omitted, right?
He weighs merely [Number] kilograms