Why exactly do you need weights? Are the responses means of a bunch of different values? If the only problem is unequal sample sizes then you should be fine as long as you feel you can assume constant variance for each group.
You can use a type 2 or type 3 SS Anova (found in the car package) that deals specifically with this issue of unbalanced data(by default the anova function in the base package does type I SS. I would suggest you read up on type I,II,II SS to see which one would be appropriate for you. There are no hard rules to this decision and much debate in the statistics community around this.