"rubbery" glue adhesives?

i'm doing a balsa wood project and i need to be able to create friction between the unfinished balsa wood and the painted wooden surface of the table. the rule book states that i can use any "glue" so i was wondering if there was an ideal "rubbery" glue that i could use. preferrably, it would bond well with the balsa wood but also create a lot of friction on the table so the structure won't move. There will be 50 pound weights involved so the balsa wood will have plenty of force to push down on the table, i just need a glue that won't slip and/or deform to much