Security assessment between $g^{a_ix_i+r_i}$ and $g^{x_i+r_i}$ Imagine a tagging system whose security requirements imply to learn nothing from the tag about the encoded value. 

We consider a plaintext space $X \in \mathbb{Z}_p$ and a group $\mathbb{G}$ where the DLP is computationally hard. 

The sender sends $\sf{tag_1}=g^x_i$ where $g$ is a generator of $\mathbb{G}$. This is not really secure in the sense that we provide the attacker an oracle to verify its guess on values in $X$. 

We change the tag to be of the form $\sf{tag_2}=g^{x_i+r_i}$ where $r_i$ is a random value from $\mathbb{Z}_p$

We consider another tagging scheme where $\sf{tag_3}=g^{a_ix_i+r_i}$ where $a_i, r_i$ are random values from $\mathbb{Z}_p$

Is $\sf{tag_3}$ more secure than $\sf{tag_2}$? Is there an attack in $\sf{tag_2}$ which is mitigated with $\sf{tag_3}$?
It is not entirely clear what your exact security requirements are and for which purpose you require this construction. I assume that the tags can not be manipulated by an adversary, e.g., are signed, and that users do not try to change their choice of $x_i$ after having a tag. Anyways, I give it a shot (although I may be wrong due to some information I do not have):

First Construction

Clearly, for the first construction you can simply try guessing $x_i$ and test against $g^{x_i}$ (which will be problematic if your $x_i$ come from a small set).

Second Construction

For your second construction, if $g^{\sum r_i}$ is revealed, then you can again test: Lets say for simplicity you have only one tag, then given the aggregate of the $r_i$ values (which happens to be $g^{r_1}$), you can just guess $x_1$ and test as in the first construction. Clearly, if there is more than one tag you can also test by cancelling out $g^{\sum r_i}$ from the aggregate of all tags, but the sum $x_1+\ldots+x_n$ in the remaining value $g^{\sum x_i}$ may not be unique anymore (so it depends if the $x_i$ can only take some specific values - then your sum could be unique but it must not be the case). 

Thrid Construction

For the third approach with tags of the form $g^{a_ix_i +r_i}$: If the value $a_i$ is uniformly at random chosen by every user, then even when publishing $g^{\sum r_i}$ this will not give an advantage for testing, as even when cancelling out $g^{\sum r_i}$ in the full aggregate of all tags you still have $g^{\sum a_i x_i}$. Without knowing any of the $a_i$ values, you cannot test anymore (this is even unconditional hiding - for uniformly random $a_i$, the value $g^{a_i}$ is a random element and so is $(g^{a_i})^{x_i}$). So your last construction is secure even if the values $x_i$ are known to come from a small set (clearly, assuming that the values $g^{a_i}$ are not available to the adversary).