There are two theoretical issues raised by your question.
1. No units of happiness, utility, or other states of mind exist. While one can understand the meaning of the claim that $2,000 is twice $1,00, one can’t make sense of the claim that one state of mind is twice another.
2. The law of diminishing marginal utility states that the subjective value of the first unit of a good is preferred to the subjective value of the second unit of a good, and so on. So, the happiness a person attaches to the first $1,000 is higher than the happiness of the second $1,000. Twice as much money, then, would not make a person twice as happy (assuming it makes sense to say “twice as happy”).