Define a "few" drinks
If you're used to running carbs you may rightly feel a bit tired the first few weeks of going paleo, and the alcohol certainly won't help with that at all. However, with regards to weight gain, are you doing any physical activity? At the end of the day total calories still matter (I'm talking fat/carbs; proteins make things a little more complicated), so watch types of food AND amounts.
1) eat real food - more vegetables, moderate meat, moderate fruits, less grains, less sugar, less vegetable oils.
2) exercise - moderate intensity cardio, sprinting, heavy lifting, dedicated stretching and mobility.
3) live - relax, de-stress, meditate.
Disclaimer: I'm not professionally qualified to make any formal recommendations. I've just done my homework and I'm my own guinea pig. All of my data, unless otherwise cited, comes from a sample size of n=1 (me).