This from AHD:
Summer:

1. A heavy horizontal timber that serves as a supporting beam, especially for the floor above. 2. A lintel. 3. A large, heavy stone usually set on the top of a column or pilaster to support an arch or lintel.
Middle English, beam, pack animal, from Anglo-Norman sumer, from Vulgar Latin *saum rius, from Late Latin sagm rius, pertaining to a packsaddle, packhorse, from sagma, packsaddle. See sumpter.

The term 'breastsummer' or 'bressumer' appears to have been used mainly in connection with fortification works; castles and like structures. I guess that the term 'breastsummer' was used for a supporting beam at around breast height. Or could it have been a beam at ground level supporting 'breastwork' (a breast-high defensive wall)?