  The $r$-color size-Ramsey number of a $k$-uniform hypergraph $H$, denoted by
$\hat{R}_r(H)$, is the minimum number of edges in a $k$-uniform hypergraph $G$
such that for every $r$-coloring of the edges of $G$ there exists a
monochromatic copy of $H$. In the case of $2$-uniform paths $P_n$, it is known
that $\Omega(r^2n)=\hat{R}_r(P_n)=O((r^2\log r)n)$ with the best bounds
essentially due to Krivelevich. In a recent breakthrough result, Letzter,
Pokrovskiy, and Yepremyan gave a linear upper bound on the $r$-color
size-Ramsey number of the $k$-uniform tight path $P_{n}^{(k)}$; i.e.
$\hat{R}_r(P_{n}^{(k)})=O_{r,k}(n)$. Winter gave the first non-trivial lower
bounds on the 2-color size-Ramsey number of $P_{n}^{(k)}$ for $k\geq 3$; i.e.
$\hat{R}_2(P_{n}^{(3)})\geq \frac{8}{3}n-O(1)$ and $\hat{R}_2(P_{n}^{(k)})\geq
\lceil\log_2(k+1)\rceil n-O_k(1)$ for $k\geq 4$.
  We consider the problem of giving a lower bound on the $r$-color size-Ramsey
number of $P_{n}^{(k)}$ (for fixed $k$ and growing $r$). Our main result is
that $\hat{R}_r(P_n^{(k)})=\Omega_k(r^kn)$ which generalizes the best known
lower bound for graphs mentioned above. One of the key elements of our proof is
a determination of the correct order of magnitude of the $r$-color size-Ramsey
number of every sufficiently short tight path; i.e.
$\hat{R}_r(P_{k+m}^{(k)})=\Theta_k(r^m)$ for all $1\leq m\leq k$.
  All of our results generalize to $\ell$-overlapping $k$-uniform paths
$P_{n}^{(k, \ell)}$. In particular we note that when $1\leq \ell\leq
\frac{k}{2}$, we have $\Omega_k(r^{2}n)=\hat{R}_r(P_{n}^{(k, \ell)})=O((r^2\log
r)n)$ which essentially matches the best known bounds for graphs mentioned
above. Additionally, in the case $k=3$, $\ell=2$, and $r=2$, we give a more
precise estimate which implies $\hat{R}_2(P^{(3)}_{n})\geq \frac{28}{9}n-O(1)$,
improving on the above-mentioned lower bound of Winter in the case $k=3$.
