No, you can support as many proposals as you want and your weight will be the same for each of them.

Let's say the HiveBuzz proposal has 1000 HP support and the stabilizer has 2500 HP support

You have 2000 HP in your wallet and want to support the HiveBuzz proposal and you vote for it (good boy 👍).
Its new support level is now 3000 (1000 + 2000) which is above the 2500 HP of the stabilizer so HiveBuzz should be funded.

But at the same time you vote for the stabilizer proposal.
Its new support level is now 4500 (2500 + 2000). By doing so, you raised again above the HiveBuzz proposal, which therefore is back defunded.