The factors of global climate change specifically affect crop and weed performance. Peas (Pisum sativum L.), spring barley (Hordeum vulgare L.), and wild mustard (Sinapis arvensis L.) were exposed to elevated atmospheric CO2 concentration ([CO2]) (1400 or 700 vs. 400 μmol mol−1) and air temperature (25/18 vs. 21/14°C, day/night) to study the single and combined effects on plant growth, photosynthetic performance, and carbohydrate metabolism. Significantly greater stimulation of the photosynthetic rate was determined at the corresponding growth CO2 concentration (Agrowth), and water use efficiency (WUE) and biomass production were detected for crops than for weed exposed to elevated [CO2]. The possibilities to translocate total soluble sugars (TSS) and starch into roots are considerably higher for crop species, especially N2–fixing pea plants compared with wild mustard, while the accumulation of photosynthates in leaves of wild mustard led to higher photosynthetic downregulation and considerably lower stimulation of Agrowth. Moreover, an increase in WUE was completely eliminated at 4°C above ambient air temperature ([25/400]) in wild mustard grown under elevated [CO2], while crops still maintained slightly higher WUE. These findings suggest that investigated crop species, especially pea plants, have higher advantage than weed under rising [CO2], and this benefit is detected to be even higher under elevated [CO2] and temperature.