Cellulose acetate is used in many applications, including for cigarette filters. Unfortunately, unlike cellulose, its (bio)degradability is under question, yet it often ends up uncontrolled in the natural environment. The main purpose of this study is to compare the effects of weathering on two types of cigarette filter (classic filters and newer filters that have more recently arrived on the market) following their use and disposal in nature. Microplastics were prepared from polymer parts of used (classic and heated tobacco products—HTP) cigarettes and artificially aged. TG/DTA, FTIR, and SEM analyses were performed both before and after the aging process. Newer tobacco products contain an additional film made of a poly(lactic acid) polymer which, like cellulose acetate, burdens the environment and poses a risk to the ecosystem. Numerous studies have been conducted on the disposal and recycling of cigarette butts and cigarette butt extracts, revealing alarming data that have also influenced the decisions of the EU, who addressed the disposal of tobacco products in the EU Directive (EU) 2019/904. Despite this, there is still no systematic analysis in the literature evaluating the impact of weathering (i.e., accelerated aging) on the degradation of cellulose acetate in classic cigarettes compared with that in newer tobacco products that have recently appeared on the market. This is of particular interest given that the latter have been promoted as being healthier and environmentally friendly. The results show that in cellulose acetate cigarette filters the particle size decreased after accelerated aging. Also, the thermal analysis revealed differences in the behavior of the aged samples, while the FTIR spectra showed no shifts in the position of the peaks. Organic substances break down under UV light, which can be seen by measuring the color change. The PLA film was found to be more stable than cellulose acetate under the influence of UV light.