Your Tab 3 only has a dual-core processor and 1GB of RAM. Both are huge bottlenecks to performance. Especially the RAM, as the lack of RAM causes Android to continually shut down processes in order to free up more RAM for the apps you're using. The fact Touchwiz is on there doesn't help matters, as Touchwiz is likely consuming a quarter of the available RAM by itself.
Neither issue is something you can correct. A factory reset may help in the short term, but the reality is that in short order you will be back in this situation again. Thus, replacing the tablet with something newer is your best option.