It's a bird, it's a plane, it's...no wait, it's just a plane.

Doubling the mass doubles the amount of lift (force) required. Since lift is proportional to the square of the velocity, doubling lift is just sqrt(2) times original velocity.

If we increase the size of the airplane by $2$ , the mass increases by $8$ while its wings area increases by $4$ . Therefore the pressure difference between the top and bottom of the wings must increase by a factor of $2$ to compensate for the additional gravitational force. To get the pressure to increase by $2$ the velocity should increase by $\sqrt{2}$ (since $p \sim \rho v^2$ via Bernoulli's equation).

The lift force L of the airplane must be equal to the weight W. The lift force L = Cl . ½ ρ.V^2. S, where Cl and S are the lift coefficient, and the wing area respectively. According to similarity concept if the size is scaled up by a factor of two. The area increases 4 times, and the mass 8 times. So to be able to lift up the new weight, the speed V has to be increased a a factor of √2 or 1.414. So the airoplane need a more powerful engine

It is unlikely that an airplane flies only using the Bernoulli effect. However, the dominant mechanism of pressure due to deflection of air obeys a similar equation: $F = \frac{dp}{dt} = \frac{dm}{dt} v \propto A \rho_{\text{air}} v^2 \propto d^2v^2.$ The vertical component of this force balances the gravitational force: $F \propto \rho_{\text{plane}} V g \propto d^3.$ Equation these, we see that $d^2v^2 \propto d^3$ so that $v \propto \sqrt{d}$ .

Doubling the dimensions $d$ results in multiplication of $v$ by $\sqrt 2\approx \boxed{1.414}$ .

Bernoulli's equation states that,

$P_1 + \rho g y_1 + \frac {1}{2} \rho v^2_1$ = $P_2 + \rho g y_2 + \frac {1}{2} \rho v^2_2$

In this case,

$P_1 = P_2$ and the density $\rho$ is constant throughout.

We can simplify the equation to,

$y_1 + \frac {1}{2} v^2_1$ = $y_2 + \frac {1}{2} v^2_2$

since the height increased by a factor of 2,

the velocity should increase by a factor of $\sqrt{2}$

Therefore $\frac {v_1}{v_0} = \sqrt{2}=1.414$