On average, 30% of a woman’s bodyweight is composed of muscle, while men have around 40%. Women actually gain a bit more muscle, percentage-wise, initially, but the absolute amount of muscle gained is still higher in men. Also, women have a harder time gaining muscle long term compared to men, so men will ultimately build even more muscle (though this long-term advantage is not proven as both women and men build muscle initially despite men having 1000 times more testosterone).
The few women who reach a level of muscularity that makes them look “bulky” are both genetically gifted and have been training very hard with the goal of acquiring this look.
Weight training will instead aid you in losing fat and building muscle. If anything, 1 kg of extra fat will make you look bulkier than adding 1 kg of extra muscle. If your training happens to make you look “too bulky” as a woman, you need only reduce your training and your body will readapt with less muscle mass.
Source 1: Janssen I et al. Skeletal muscle mass and distribution in 468 men and women aged 18-88 yr. J Appl Physiol (1985). 2000 Jul;89(1):81-8.
Source 2: Kvorning T et al. The activity of satellite cells and myonuclei following 8 weeks of strength training in young men with suppressed testosterone levels. Acta Physiol (Oxf). 2015 Mar;213(3):676-87.