Yes, of course, women should be training with weights there are no limits. Most women shy away from weight training assuming that they will put on muscle like men and will compromise their female characteristics. Let's talk science; women don't produce enough testosterone naturally in their body which is responsible for maintaining a more massive masculine structure, unlike men. Even for men, if they want to get to a more significant mass ratio, they have to follow a very high calorie and protein diet for an extended period along with many supplements and induce different methods of training routine to induce muscle hypotrophy (muscle growth). Now another reason why women assume they will buff up like men is due to several pictures of highly built women bodybuilders making rounds online let me clear they are that way because they have chosen to be like that by taking several growth hormones and steroids, it can be due to their nature of career or personal reasons. Apart from all these positive benefits such as it increases your metabolism, bone density, efficiently burns fat round the clock, improves hormonal functions, gives you a better body posture etc. negatives are close to none. The only thing that varies is a well-planned diet. So don't worry you can lift as much as you want but keep in mind a routine of cardio respiratory Fitness is also Important. According to the American college of sports medicine make sure you're getting at least 150-250 minutes of cardio every week.