This is what Webster has to say about "support." I find a lot of possible "bleed over" in some of the defenitions.

<font color="purple">Support: transitive verb

1 : to endure bravely or quietly : BEAR
2 a (1) : to promote the interests or cause of (2) : to uphold or defend as valid or right : ADVOCATE (3) : to argue or vote for b (1) : ASSIST, HELP (2) : to act with (3) c : to provide with substantiation : CORROBORATE [support an alibi]
3 a : to pay the costs of : MAINTAIN b : to provide a basis for the existence or subsistence of [the island could probably support three -- A. B. C. Whipple]
4 a : to hold up or serve as a foundation or prop for b : to maintain at a desired level by purchases or loans; also : to maintain the price of by purchases or loans
5 : to keep from fainting, yielding, or losing courage : COMFORT
6 : to keep (something) going (keep WHAT going?) (italics mine)
synonyms SUPPORT, UPHOLD, ADVOCATE, BACK, CHAMPION mean to favor actively one that meets opposition. SUPPORT is least explicit about the nature of the assistance given [supports waterfront development]. UPHOLD implies extended support given to something attacked [upheld the legitimacy of the military action]. ADVOCATE stresses urging or pleading [advocated prison reform]. BACK suggests supporting by lending assistance to one failing or falling [refusing to back the call for sanctions]. CHAMPION suggests publicly defending one unjustly attacked or too weak to advocate his or her own cause [championed the rights of children].</font>