I'd say it really depends on how you box and how your body will take the weights.

If you feel you NEED power for your whole game to work then yeah go for the weights but if you feel you have enough speed and technique to be able to box well i'd say just work hard every session.

I've been doing weights properlly for the past couple of weeks and i can say i dont feel that much stronger in the sense that i feel like i can punch any harder then before and my arms have just defined rather then got any bigger, but thats down to my muscle tissue.

I'd also say work on technique, you say you only been boxing solid for only a month, it will take longer then that to iron everything out. Develop new ways in which you feel your punches have more impact.