Simply by the fact that the languages both have a common ancestor after common proto-indo-european. There is a similar situation where the Celts and the Italic peoples split in a similar fashion. The Celto-Italic connection is something that can be proven by geographic distribution, where the only dividers were the Etruscans, a non-Indoeuropean people. Also, the old gods are frightfully similar. Perkunas and Perun are good examples of similarly named gods filling the same roles. The similar religions, as well as even words (человек in Russian to cilveks in Latvian), suggests that there indeed was a deeper connection between Slavs and Balts. The evidence to support it is there. However, I am once again going to concede that this is all very much part of linguistic and anthropological theory. It’s not set in stone because of the fact that so little documentation, if any, exists from the time that this Balto-Slavic group possibly even existed. A better way to put forward my position, then, is to say that I agree with the theory of the Balto-Slavic group.